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SOURCEBOOK ON 

atomic energy 


by 

SAMUEL GLASSTONE 


Consultant io the 


United States Atomic Energy Commission 


MACMILLAN 
ST. MARTIN’S 


CO. limited 
street, LONDON 


1957 



MACMILLAN AND COMPANY LIMITED 
London Eotnbtty CaleuUt Madras Melbourne 

THE MACMILLAN COMPANY OF CANADA LIMITED 
Toronto 

ST martin's press INC 
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This book u copyright ttt all countries ttkteh 
art stgnatortes to the Bertu Convention 
First British Edtiton T953 
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COPYRIGHT IN U S A BY 
D VAN NOSTRAND CO INC 


MBtl LlBRnRY 



PRINTED IN THE NETHERLANDS 
BY MESSRS JAN DE LANCE, DEVENTER 



Foreword 


Early in 1948 the American Textbook Publishers Institute requested the 
Atomic Energy Commission to prepare a comprehensive sourcebook on atomic 
energy for the use of textbook authors and editors. The Commissioi^ recognized 
the need for such a volume, and for the preparation of the manuscript obtained 
the services of Dr. Samuel Glasstone, outstanding scientist and author in 
chemistry and related fields, who prepared the book at the instance of the 
Commission. 

In his search for background material for the Sourcebook, Dr. Glasstone 
studied the work in the Commission’s various laboratories and the files of re- 
ports on scientific work. The manuscript was reviewed by a number of scien- 
tists associated with the national atomic energy program for technical accuracy 
and to obtain the benefit of any suggestions they might wish to offer. It was 
also reviewed by the Atomic Energy Commission, Office of Classification, to 
make certain that the publication would in no way jeopardize national security. 
The presentation of the material in this book and its scientific evaluation are 
wholly the work of Dr. Glasstone. 

The Commission “wishes to acknowledge the assistance andi cooperation of 
the American Textbook Publishers Institute both in planning the Sourcebook 
and in reviewing the completed manuscript. While originally planned for a 
specific purpose suggested by the Institute, Dr. Glasstone has written a book 
which is of far broader usefulness and which provides a source of basic atomic 
energy information for everyone interested in this field. 



CHAIRMAN, UNITED STATES ATOMIC ENERGY COMMISSION 



Acknowledgment 


The writer wishes to record his indebtedness to the following who either read 
portions of the manuscnpt and made valuable comments, or who supplied in- 
formation which has been used in the book 
P C Aebereold, M Calvin, W D Claus, A H Compton, L G Cook, C D 
Coryell, A Dahl, N Feather, W F Libby, G Manov, C Mbller, P B Pearson, 
I Perlman, G T Seaborg, R C Smith, F H Speddmg, R W Stoughton, 
W H Sullivan, R L Thornton, C A Tobias, E A WiggmandN H Woodruff 
Special thanks are due to Carl B Holmes, U S Atomic Energy Commission, 
Oak Ridge, for his handling of the art work, to Daniel J Pflaum, Chief, Mater- 
ials and Information Branch, Division of Research, A E C , for many useful 
suggestions, and to Alberto F Thompson, Chief, Technical Information Service, 
A E C , and his assistant, John H Martens, for their continued encouragement 
and cooperation, without which the production of this book would have been a 
much more difHcult undertaking 

Fmally, the author must express his indebtedness to his wife for her help m 
the collection of matenal, m the revision and preparation of the manuscnpt for 
the press, and m the numerous tasks that are involved m the wnting of a book 


Oak Rtdge, Tenn 
July 1960 


SAilUEL GLASSTONE 



Contents 


CHAPTER PAGE 

' I. Foundations of the Atomic Theory 1 

11. Constituents of the Atom 23 

•III. Energy and Radiation 58 

IV. The Structure of the Atom 85 

' -V. Natural Radioactivity 109 

VI. Measurement of Radioactivity 130 

' VII. Nuclear Radiations 149 

. VIII. Isotopes 175 

IX. The Acceleration of Charged Particles 213 

X. Nuclear Transmutation and Artificial Radioactivity. . . . 245 

XI. The Neutron 284 

XII. Nuclear Structure and Nuclear Forces 317 

"XIII, Nuclear Fission 344 

XIV. The Utilization of Nuclear Energy 371 

XV. The New Elements 414 

XVI. The Uses of Isotopes 439 

XVII. Cosmic Kays and Mesons 475 

XVIII. Radiation Protection and Health Physics 500' 

Name Index 527 

Subject Index 532 



iSowrccBoofc on Atomic Energy 


physical chemist W Nemst stated 
that “by one effort of modem science, 
[it] arose hke a phoenix from the ashes 
of the old Greek philosophy ” That 
this IS a misconception can be proved 
by a quotation from Dalton’s Ne^ 
System of Chemical Philosophy, pub- 
hshed m 1808, in -which he discussed in 
detail his ideas concerning the atom as 
the unit of chemical structure 
1 4 In considering the existence of a 
substance such as water in gaseous 
(steam), hquid and sohd (ice) states, 
Dalton said “The observations have 
tacitly led to the conclusion which 
seems universally adopted, that all 
bodies of sensible magmtude are 
constituted of a vast number of ex- 
tremely small particles, or atoms of 
matter bound together by a force of 
attraction “ The phrase “which seems 
umversally adopted” is sigmficant, for 
it implies that the atomic concept of 
matter was already ividely accepted 
It has been suggested that Dalton was 
indebted to Newton, whose works he 
probably studied, for m his notes of a 
lecture delivered at the Royal Insti- 
tution, London, in January 1810, he 
remarked “Nevrton had demonstrated 
clearly that an elastic fluid [i e , 
a gas] IS constituted of small particles 
or atoms of matter ” 

1 6 There is no doubt, also, that the 
contemnora:^^ Irish chemists^ Biyan 
Higgms (1737-1820) and his nephew 
William Higgms (1769-1825) had ex- 
pressed themselves very clearly on the 
subject of combination by atoms some 
years prior to Dalton Why then is the 
latter regarded as the founder of the 
atomic theory? The answer lies m 
the fact that John Dalton made the the- 
ory quantitative By showing how the 
weights of different atoms relative to 
one another could be determined, he 
introduced a feelmg of reahty into a 
purely abstract idea In a paper sub- 


Chap I 

mitted to the Literary and Philosophi 
cal Society of Manchester, England, m 
October 1803, Dalton ivrote “An 
inquiry into the relative weights of the 
ultimate particles [atoms] of bodies is 
a subject, so far as I know, entirely 
new I have lately been prosecuting 
this enquiry with remarkable success ' 
Most of his weights were subsequently 
proved to be erroneous, but Dalton 
sowed the seed which grew, where 
others had previously merely turned 
over the soil 

1 6 In the Lowell Lectures on Sci- 
ence in the Modem World, delivered at 
Harvard University in 1925, the Anglo- 
Amencan philosopher and mathema- 
tician A N Whitehead said “In 
considering the history of thought, it 
IS necessary to distinguish the real 
stream, determining a penod, from the 
ineffectual thoughts casually enter- 
; tamed In the eighteenth century 
every well educated man read Lu- 
I cretms and entertained ideas about 
atoms But John Dalton made them 
efficient m the stream of science, and m 
the function of efficiency atomicity as 
a new idea The atomic theory of the 
classical thinkers was somewhat m the 
nature of a vague philosophical specu 
lation, but the theory as enunciated by 
Dalton was much more specific It 
pro-vided an explanation or, at least, an 
integjretation of many chemical facts 
and, of greater consequence, it acted as 
a guide to further experimentation and 
mvestigation 

1 7 From the tune of Dalton the 
atomic hypothesis has played an in- 
creasmgly important role m science, 
first m chemistry and later m physics 
It 13 true that a few scientists, some of 
them men of influence like the German 
physical chemist Wilhelm Ostwald, 
doubted the existence of atoms, but by 
the early years of the present century 
even these objectors were converted 



Fov/ndalions of the Atomic Theory 


Today the arguments in favor of the 
atomic structure of matter are so nu- 
merous and convincing that the con- 


cept is universally accepted as an 
established fact rather than a theory.* 


THE CHEMICAL ELEMENTS 


The Foxje-Element Theoey 

1.8. While the atomic concept was 
undergoing development, another 
important principle, also based on 
Greek philosophy, was being refined in 
the fire of successive generations of the 
human mind. In contemplating the 
make-up of the universe, Empedocles, 
in the Mth century B.C., entertained 
the idea that all matter was composed 
of four “elements,” namely, fire, earth, 
air and water. It is probable that in 
tliis respect also, as with the atom, the 
ancient Hindu thinkers had antici- 
pated the Greeks, but our present 
views stem more directly from the 
latter than from the former. Having 
the influential support of Aristotle and 
others, the four-element theory was 
widely accepted for more than two 
thousand years, in spite of a consider- 
able degree of vagueness concerning its 
actual implications. 

1.9. Some scholars undoubtedly re- 
garded the elements as referring to 
material earth, air, fij-e and water, 
while others thought of them more in 
the nature of principles or represen- 
tations of physical attributes. Aris- 
totle, for example, envisaged all matter 
ns consisting of one primordial sub- 
stance wliich he called hyle (stuff or 
material) ;t and this could acquire 
varying amounts of the four qualities, 
or “principles,” hot, cold, dry and 
moist. Thus air was hot and moist. 


water was cold and moist, fire was hot 
and dry, and earth was cold and dry. 
The difference between one material 
and another was regarded as due to 
variations in the primal qualities, but 
the fundamental matter was always 
the same. 

1.10. It is apparently on this inter- 
pretation of the four-element theory 
that the ancient alchemists based their 
vain efforts to change common metals 
into gold. For hundreds of years all at- 
tempts to bring about transmutation 
met with complete failure, although at 
the present time, thanks to the ac- 
cumulated knowledge concerning the 
behavior of atoms, the deliberate 
change of one element into another is a 
daily occurrence in many laboratories 
(Chapter X). 

Elements and Compounds 

1.11. The first dent in the widely 
accepted, but unsatisfactory, four- 
element theory of the constitution of 
matter was made in the seventeenth 
century by the Irish-born Robert 
Boyle. In Ms book entitled The Scepti- 
cal Chymist, published in London in 
1661, Boyle rejected the idea of four 
“principles,” and condemned the al- 
chemists for their futile attempts to 
bring about the transmutation of 
metals. At the same time he gave his 
own interpretation of an element; he 
wrote: “I . . . mean by elements . . , 


^ defined as something for the actual existence of which there is definite’ evi- 
oence. A theory or hj-pothesis, on the other hand, is a purely conceptual attempt to exnlain 



2 


Sourcebock on 

physical chemist W Nernst stated 
that ‘ by one effort of modern science, 
[it] arose hke a phoenix from the ashes 
of the old Greek philosophy ’ lliat 
this IS a misconception can be proved 
by a quotation from Dalton’s New 
System of Chemical PkHosophy^ pub- 
lished in 1808, m which he discussed m 
detail his ideas concerning the atom as 
the unit of chemical structure 
1 4 In considering the existence of a 
substance such as water in gaseous 
(steam), liquid and soUd (ice) states, 
Dalton said ^'The observations have 
tacitly led to the conclusion which i 
seems uzuversally adopted, that all 
bodies of sensible magnitude are 
constituted of a vast number of ex- 
tremely small particles, or atoms of 
matter bound together by a force of 
attraction " The phrase “which seems 
umvereally adopted" is significant, for 
It implies that the atomic concept of 
matter was already widely accepted 
It has been suggested that Dalton was 
indebted to Newton, whose works he 
probably studied, for m his notes of a 
lecture delivered at the Royal Insti- 
tution, London, in January 1810, he 
remarked ‘T*Tewton had demonstrated 
clearly that an elastic fluid [i e , 
a gas} IS constituted of small particles 
or atoms of matter " 

1 6 There is no doubt, also, that the 
contemporary Irish chemists, Bryan 
Higgms (1737-1820) and his nephew 
Wilham Higgins (1769-1525) had ex- 
pressed themselves very clearly on the 
subject of combination by atoms some 
years pnor to Dalton Why then is the 
latter regarded as the founder of the 
atomic theory? The answer lies in 
the fact that John Dalton made the the- 
ory quantitative By showing how the 
weights of different atoms relative to 
one another could be determined, he 
introduced a feeling of reality into a 
purely abstract idea In a paper sub- 


Atomic Energy Chap I 

mitted to the Literary and Philosophi- 
cal Society of Manchester, England, m 
October 1803, Dalton wrote “An 
mquiry into the relative weights of the 
ultimate particles [atoms] of bodies is 
a subject, so far as I know, entirely 
new I have lately been prosecuting 
this enquiry with remarkable success ” 
Most of his weights were subsequently 
proved to be erroneous, but Dalton 
sowed the seed which grew, where 
others had previously merely turned 
over the soil 

1 6 In the Lowell Lectures on Sci- 
ence in the Modem World, delivered at 
Harvard University m 1925 the Anglo- 
American philosopher and mathema- 
tician A N Whitehead said “In 
considenng the history of thought, it 
IS necessary to distinguish the real 
stream, determining a penod, from the 
ineffectual thoughts casually enter- 
tained In the eighteenth century 
every well educated man read Lu- 
cretius and entertained ideas about 
atoms But John Dalton made them 
efficient in the stream of science , and m 
the function of efficiency atomicity w as 
a dew idea” The atomic theory of the 
classical thinkers was somewhat in the 
nature of a vague philosophical specu- 
lation, but the theory as enunciated by 
Dalton was much more specific It 
provided an explanation or, at least, an 
interpretation of many chemical facts 
and, of greater consequence, it acted as 
a guide to further expenmentation and 
investigation 

1.7 From the tune of Dalton the 
atomic hypothesis has played an in- 
creasingly unportant role in science, 

I first m chemistry and later in physics 
It 13 true that a few scientists, some of 
them men of influence like the German 
physical chemist Wilhelm Ostwald, 
doubted the existence of atoms, but by 
the early years of the present century 
even these objectors were converted 



Foundations of the Atomic Theory 


Today the arguments in favor of the 
atomic structure of matter are so nu- 
merous and convincing that the con- 


cept is universally accepted as an 
established fact rather than a theory.* 


THE CHEMICAL ELEMENTS 


The Four-Element Theory 

1.8. While the atomic concept was 
\mdergoing development, another 
important principle, also based on 
Greek philosophy, was being refined in 
the fire of successive generations of the 
human mind. In contemplating the 
make-up of the universe, Empedocles, 
in the fifth century B.C., entertained 
the idea that all matter was composed 
of four “elements,” namely, fire, earth, 
air and water. It is probable that in 
this respect also, as vdth the atom, the 
ancient Hindu thinkers had antici- 
pated the Greeks, but our present 
views stem more directly from the 
latter tlmn from the former. Having 
the influential support of Aristotle and 
others, the four-element theory was 
widely accepted for more than two 
thousand years, in spite of a consider- 
able degree of vagueness concerning its 
actual implications. 

1.9. Some scholars undoubtedly re- 
garded the elements as referring to 
material earth, air, fire and water, 
while others thought of them more in 
the nature of principles or represen- 
tations of physical attributes. Aris- 
totle, for example, envisaged all matter 
as consisting of one primordial sub- 
stance which he called hyle (stuff or 
material) ;t and this could acquire 
varying amounts of the four qualities, 
or “principles,” hot, cold, dry and 
moist. Thus air was hot and moist, 


water was cold and moist, fire was hot 
and dry, and earth was cold and d^. 
The difference between one material 
and another was regarded as due to 
variations in the primal qualities, but 
the fundamental matter was always 
the same. 

1.10. It is apparently on this inter- 
pretation of the four-element theory 
that the ancient alchemists based their 
vain efforts to change common metals 
into gold. For hundreds of years all at- 
tempts to bring about transmutation 
met with complete failure, although at 
the present time, thanks to the ac- 
cumulated knowledge concerning the 
behavior of atoms, the deliberate 
change of one element into another is a 
daily occurrence in many laboratories 
(Chapter X). 

Elements ane Compounds 

1.11. The first dent in the widely 
accepted, but unsatisfactory, four- 
element theory of the constitution of 
matter was made in the seventeenth 
century by the Irish-born Robert 
Boyle. In Ws book entitled The Scepti- 
cal Chymist, published in London in 
1681, Boyle rejected the idea of four 
“principles,” and condemned the al- 
chemists for their futile attempts to 
bring about the transmutation of 
metals. At the same time he gave his 
own interpretation of an element; he 
wrote: “I . . . mean by elements . . . 


A fact be defined as something for the actual existence of which there is definite evi- 
f is a purely conceptual attempt to explain 
WWo facts are presumably established and unalterable, a theory 
mav be altered or discarded if it prov'es to be inadequate. 

chang^, possibly by Roger Bacon in the thirteenth century, to 
proJyfc, from -protos and hyU, meaning the first or primal matter. ^ 



4 


SouTcehooh on Atomic Energy Chap I 

certain primitive and simple, or per^ the Swedish chemist J J Berzelius had 
fectly unmingled bodies, which not increased the number of elements to 
being made of any other bodies, or of fifty, and at the present time ninety 
one another, are the ingredients of different elements are defimtely known 
which mixt bodies are immedi- to exist on the earth, while eight more 
ately compounded, and into which have been obtained by other means, as 
they are ultimately resolved I will be explained in Chapter XVI All 
must not look upon any body as a true material things contain at least one of 
principle or element which is not thtse elements, and when two or more 
perfectly homogeneous, but is further elements unite with one another, by 
resolvable into any number of distinct the process referred to as chemical 
substances, how small soever ” combination, the resulting product is 

1.12. In these v. ords of Robert known as a compound 
Boyle lay the germ of the present day 

significance of the term element, but Definition of an Element 
more than a hundred years elapsed 1.14. Until the beginning of the 
before the ideas ho expressed can be present century a chemical element 
said to have had any real influence on would have been defined simply as a 
scientific thought It was only after form of matterwhich could not besplit 
the French chemist A L Lavoisier up into other forms of matter Now, 
proved m 1774 that air was not a aim- with the discovery of the phenomena 
pie elementary substance, but a imx- of radioactivity, accompanied by the 
ture of at least two different gases, now spontaneous change of one element 
called nitrogen and oxygen, and after into another (Chapter V), and the de- 
the work, m 1781, of Joseph Priestley velopment of venous means of brmg- 
and of Henry Cavendish, in England, ing about transmutation and disinte- 
established the fact that water was gration of numerous elements (Chapter 
compounded of hydrogen and oxygen, IX), it is not easy to give such a precise 
that the four-element theory was fi- definition It will be seen, in succeed- 
nally abandoned In its place, Lavoi- mg chapters, that radioactive changes 
sier established, m 1789, the modem are spontaneous and cannot be con- 
concept of an element, thus “We trolled by any known procedures, while 
apply the term elements to bod- most disintegration and transmutation 
les to express our idea of the last point reactions are associated with electn- 
witfci rs capabfe a/ feacirmg ” i csily cdi&rged p&rtides h:gh 

An element was thus regarded as a energy Chemical processes, on the 
substance containing, as far as was other hand, involve energy changes of 
known, only one kind of matter, and a low order of magnitude, so that it is 
which could not be split up in any possible to describe an element as a 
known way into anything simpler form of matter which cannot be de- 

1.13. On this basis, Lavoisier sub- composed into, nor be produced from, 
stituted for the four elements of the simpler fonns of matter by means of 
Greek philosophers a list of nearly ordinarT/ chemical reactions In spite of 
thirty elementary substances, of which the somewhat vague character of this 
more than twenty are still regarded as definition,* there is never any doubt at 
elements even to this day By 1819, the present time concerning the ele- 

• An element may be defined more precisely as a form of matter all the atoms of which 
have the same nuclear charge (Chapter IV) 


5 


Foundations of the Atomic Theory 


mentary or compound natiire of a, | 
material. ISlumerous tests, now avail- 
able, based on characteristic physical 
properties, such as the optical spec- 
trum, mass spectrum and X-rays, per- 
mit elements to be distinguished and 
identified. 

1,16. The atom may How be defined 
as the smallest possible or ultimate 
particle of an element, each element 
ha\dng its oum characteristic atoms. 
As udll be seen in Chapter IV, the atom 
itself has an internal structure and can 
be split up into subatomic particles. 
But these particles, most of which are 
electrical in nature, do not have the 
characteristic properties of the ele- 
ment. In the sense that the identity of 
the element is to be retained, the atom 
may therefore be regarded as indi- 
Nusible. 

Symbols and Fokmulas 

1,16. In order to represent pictori- 
ally the building up of compounds from 
elements, Dalton introdiiced a set of 
symbols for the atoms. Thus, an atom 
of oxygen was indicated by a circle, one 
of hydrogen by a circle with a central 
dot, and a nitrogen atom was repre- 
sented by a circle with a vertical line 
through it. This type of formulation 
was not only somewhat cumbersome 
when compounds were being consid- 


ered, but the discovery of each new 
element presented the problem of in- 
venting an appropriate symbol. I^e 
difficulty was overcome by Berzelius 
who devised the method "which forms 
the basis for the symbolic represen- 
tation of elements and compounds in 
use at the present day. 

1.17. In his treatise On the Theory 
of Chemical Proportions (Paris, 1819), 
Berzelius proposed that “chemical 
symbols should be letters of the alpha- 
bet, in order to be easily drawn and 
printed without disfiguring the text,” 
and that “the initial letter [or letters] 
of the Latin name of each element” 
should be used for this purpose. Con- 
sequently oxygen (oxygenium) was 
symbolized by O, hydrogen (hydroge- 
nium) by H, copper (cuprum) by Cu, 
gold (aurum) by Au, silver (argen- 
tum) by Ag, and so on.* The symbol, 
or formula, as it is generally called, of a 
compound is then obtained by com- 
bining the symbols for the appropriate 
elements, with subscripts to indicate 
the numbers of atoms involved. Thus, 
the formula for water, which involves 
a chemical union of two atoms of hy- 
drogen with one of oxygen, is H2O; 
sulfuric acid, containing two atoms of 
hydrogen, one of sulfur and four of 
oxygen, has the formula H2SO4, and 
so on. 


THE DETERMINATION OF ATOMIC WEIGHTS 


DajjTon’s Atomic W^eight System 

1.18. As mentioned earlier, perhaps 
Dalton’s most significant contribution 
to the atomic theory was his attempt 


to determine the relative masses or 
weights! of atoms. The actual atoms 
are, of course, much too small to be 
weighed directly, and so it is con- 


* Some .symbols, e.g., 0 and H, were obtained from Latinized names of French or otbor 
onrin. Tlie complete list of modem sj'mbols for the elements is given in 5 1.37 
T Although mass and weight are treated here as synonymous, it is strietlv snunlrlno- non.,,. 
Bam to make a distinction. Mass is a measure oPtee Vn«ty oPStoinTfedv whi?; 
weight IS the force ^erted by the body, under tha influence of It Ls bemmrSe 

S4Te mass#’ wSd pet45 ^more 



6 Sourcebook on 

vement to express their weights rels^ 
tive to that of a specified atom For 
this purpose Dalton chose the atom of 
hydrogen, the hghtest atom known to 
h»m and, as it happens, the hghtest of 
all the elements Hence, to the hy- 
drogen atom was ascribed a weight of 
unity, and the weights of other atoms 
were then recorded in terms of that of 
the hydrogen atom 

1 19 The actual procedures for ob- 
taimng the relative atoimo weights 
were then based on certain postulates 
concerning the nature of atoms and 
their mode of combination The fol- 
lowing quotations from Dalton’s New 
System of Chemical Philosophy, men- 
tioned earlier, give the arguments m 
his own words 

“Whether the ultimate particles of 
a body, such as water, are all alike, 
that IS of the same figure e , size 
and shape], weight, etc , is a question 
of some importance From what is ! 
known, we have no reason to appre- 
hend a diversity m these particulars 
if it does exist m water, it must equally | 
exist in the elements constituting 
water, namely, hydrogen and oxygen 
Now it IS scmiely possible to conceive 
how the aggregates of dissimilar parti- 
cles should be so uniformly the same 
Therefore we may conclude that 
the ultimate particles of all homogene- 
ous bociies are perfecfiy afike m weight, , 
figure etc In other words, every [ulti- 
mate] particle of water is hke every 
other particle, every [ultimate] par- 
ticle of hydrogen is hke every other 
particle of hydrogen, etc 

“Chemical analysis and synthesis go 
no further than to the separation of 
particles from one another, and to their 
reumon No new creation or destruc- 
tion of matter is within the reach of 
chemical agency All the changes 
we can produce consist m separating 
particles that are in a state of cohesion 


Atomic Energy Chap J 

or combmation, and joining those that 
are previously at a distance 

“If there are two bodies, A and B, 
•which are disposed to combine, the 
following IS the order in which com- 
binations may take place, beginning 
wuth the most simple namely, 1 atom 
of A -b 1 atom of B [= AB] , 1 
atom of A + 2 atoms of B [— ABj] 
, 2 atoms of A 4- 1 atom of B 
[= AjB], etc “ 

1 20 Stated briefly, Dalton's con- 
clusions were threefold that the ulti- 
mate particles of a given pure sub- 
stance, whether element or compound, 
are alike m size, shape and weight, that 
chemical reaction does not cause any 
change m the nature of atoms but 
results merely m their rearrangement, 
and, that combination between atoms 
takes place m the ratio of the simplest 
numbers, preferably AB, then ABj 
and so on If, as Dalton supposed, the 
atoms of a given element are all alike 
and axe unchanged by chemical action, 
then the relative weight of the atom, 
as determined from the analysis of a 
compound, should have a de^ite and 
constant value While the actual de- 
termination of relative atomic weights 
made use of the third of the postulates 
stated above, the results could have no 
significance without the first two 

1 21 The procedure used by Dalton 
may be if/ustrated by reference to fic? 
estimate of the atomic weight of oxy- 
gen At the time only one compound 
of oxygen with hydrogen — ^water — ^was 
kno^m, and so Dalton, m accordance 
with the pnnciples he enunciated as- 
sumed it to have the simplest possible 
composition, namely, the combination 

I of one atom of hydrogen with one of 
o^gen, 1 e , HO Upon analysis he 
I found that water consisted of one part 
I by weight of hydrogen and seven— 

! laterfoundtobeei^t — ^parts by weight 
1 of oxygen It followed, therefore, that 



Foundoilons of the Aioniic Theory 


il the -weight of hydrogen is taken 
as unity, the relative atomic weight 
of oxygen should be seven actually 
eight. ‘ That is to say, the weight of a 
single atom of oxygen, according to 
Dalton, was seven — actually eight 
times that of a single hydrogen atom. 
Similarly by assuming the formula of 
ammonia to be NH, the atomic weight 
of nitrogen appeared to be five — more 
accurately 4.7 — ^relative to that of hy- 
drogen. 

Combining ob Equivalent 
Weights 

1.22. Apart from the errors in Dal- 
ton’s experimental work, several of his 
atomic weights, such as those of oxy- 
gen and nitrogen given above, were 
incorrect. The reason for the discrep- 
ancies lay in the fact that the postu- 
lated simple formulas of the type AB, 
such as, HO for water and NH for 
ammonia, were erroneous; water is 
now knoum to be properly represented 
by HjO and ammonia by NHs. What 
Dalton deteimined was, in general, the 
comUning weight or equivalent weight 
of an element, that is, the weight of 
the element which combines -with or 
replaces — that is, is equivalent to — 
one part by weight of hydrogen.* 

1.23. If the formula of the com- 
pound under consideration is actually 
HX, as is the case, for example, when 
X is the element chlorine, then the 
atomic and combining weights are 
identical. In other instances, however, 
the atomic weight is a simple multiple 
of the equivalent weight. It can be 
readily seen that this multiple must be 
the same as the number of atoms of 
hydrogen which unite -B-ith, or replace, 
one atom of the given element. Thus, 
since the formula of water is HiO, and 


two atoms of hydrogen eombine with 
one of oxygen, the atomic weight of 
oxygen is exactly twice the equivalent 
weight. If, therefore, Dalton had used 
the correct formula for water, he would 
have arrived at an atomic weight of 
tivice seven, i.e., 14, relative to hydro- 
gen, which is in fair agreement with the 
more accurate value of 16. Similarly, 
if he had known that ammonia was 
NHs, the atomic weight of nitrogen 
would have been given as three times 
five, i.e., 15, not very different from 
the accepted atomic weight of approxi- 
mately 14. 

The Atomic Weight Scale 

1.24. It is evident from the figures 
just cited that Dalton’s experimental 
work was not too reliable. One of the 
factors responsible was his choice of 
hydrogen as the basis of comparison 
for atomic weights. In the first place, 
relatively few elements form com- 
pounds with hydrogen, and these are 
not easy to analyze; in the second 
place, on account of the lightness of 
hydrogen, a small error in weighing 
leads to a large over-all discrepancy. 
Since most elements combine with oxy- 
gen, the atom of which is about six- 
teen times as hea-vy as that of hydro- 
gen, Berzelius used oxygen as the 
standard, assigning to it an arbitrary 
combining weight of 100. Later there 
was a return to the Daltonian system 
and the weight of the atom of oxygen 
was then found to be very close to 16, 
in comparison with unity for hydrogen. 
Because of its practical value, as indi- 
cated above, chemists therefore agreed 
to take the atomic weight of oxj'^gen, 
as it occurs in the air, to be exactly 
16.000, and its equivalent weight to be 
• 8.000; this is still the basis of mod- 


of combining (or equivalent) weight of an element uses 8.000 parts 
> weight of oxy gen, rather than 1 part of hydrogen, as the basis of comparison (§ 1.24), 



8 


Sourcehooh on Atomic Energy 


ern chemical atomic and equivalent 
weights* The atomic weight of hydro- 
gen on this scale is now known to be 
3 0080, rather than exactly unity 

Atomic aiid Equivalent Weights 
1 25 In Dalton’s time the pnnciples 
of quantitative chemical analysis were 
not well understood, and the precision 
balance had not been developed, so 
that combining weights of a high or- 
der of accuracy could not have been 
expected With improvements m the 
techniques and methods of analytical 
chemistry during the first half of the 
nineteenth century, there became avail- 
able increasingly exact values of the 


Cha-p 1 

combimng or equivalent weights cf 
many elements, for which J J Ber- 
zehus, m Sweden, and J S Stas, n 
Belgium, were largely responsibh 
Before these could be converted into 
atomic weights there still existed die 
problem of finding for each element 
the integer by which the equivalent 
weight was to be multiplied In this 
connection, Berzelius obtamed guid- 
ance from the hw of tsomarphismf 
proposed by his German pupil E 
Mitscherlich m 1819, as well as from 
the law of the constant heat capacity of 
atomsj discovered m the same year by 
the French scientists P L Dulongand 
A T Petit 


ATOMS AND MOLECULES 


Eauly Developments 
1 26 A fundamental postulate, 
which would have been of inestimable 
value in the early attempts at dcter- 
mimng atomic weights, had been pro- 
posed independently by the Itadian 
physicist Amadeo Avogadro in 1811, 
and some three years later by A M 
Ampfere, for whom the unit of electric 
current is named Unfortunately, the 
concepts involved were not too clearly 
expressed nor too well understood until 
1858, when Stamslao Cannizzaro, in 
his Sketch of a Course of Chemical PAt- 
losopky as given in the University of 
Genoa, clarified and explained the sig- 
nificance of the ideas of his fellow coun- 
tr 3 Tnan, Avogadro, published more 
than forty years earher 


1 27. In order to appreciate the cir- 
cumstances at that time, it is necessary 
to consider the distinction between 
atom and molecule § In the early years 
of the mneteenth century no very clear 
differentiation was made Dalton, for 
example, occasionally used the term 
molecule as synonsrmous wnth his ulti- 
mate particle or atom Further, he did 
not discriminate between the parti- 
cles of an element and those of a 
compound, he referred to both types 
as "atoms ’’ Avogadro, on the other 
hand, went to the other extreme, he 
did not use the term atom, but applied 
the general name of "molecule" to 
various particles However, a careful 
reading of Avogadro’s ivntings shows 
that he distinguished between three 


* The reasons for the qualifications “as it occurs m air," applied to oxygen, and "chemical, 
applied to atoimc weight, will be given m $ 8 59 
T According to this law, isomorphous substances, i e , substances which form crystals of 
similar shape, havmg similar chemical properties can usually be represented by analogous 
formulas e g , CujS and AgiS, FejOj and AJiOa The valence of an element, i e , the ratio of 
the atomic wei^t to the equivalent weight, can be derived from the formula of an appropriate 
comnound 

t The product of the atoimc weight and the spwnfic heat has approximately the same value 
for most solid elements The specilo heat can be readily measured, and hence a rough atoimc 
weight can be estimated The accurate value can then lie obtained from the combining weight 
5 B^m the diminutive of the Latin word (mass) , hence, molecule means a amali mass 



9 


Foundoiions of the Atomic Theory 


different types of molecules, althougli 
tbe distinction is implicit rather than 
explicit. There is little doubt that the 
situation was clear in Avogadro’s mind, 
but it is not so certain that his views 
were expressed plainly enough to be 
grasped b}’- his contemporaries. In the 
succeeding decades, efforts were made 
to define the terms “atom” and "mole- 
cule,” particularly by the French sci- 
entists A. M. Gaudin (1833), A. M. 
Ampbre (1835), A. Laurent (1846) and 
C. L. Gerhardt (1856). It was Can- 
nizzaro’s logical development of the 
consequences of the distinction be- 
tween these quantities that resulted in 
the opening of a new era in the deter- 
mination oif atomic -weights. 

1.28. A molecule may be defined as 
the smallest particle of any substance 
— element or compound — as it nor- 
mally e.xists. A molecule of a com- 
pound always contains atoms of two or 
more elements; thus, a molecule of 
water is represented by H 2 O, because 
it consists of two atoms of hydrogen 
and one of oxygen. Since an atom of an 
element is indivisible, it is not possible 
for a molecule to contain less than one 
atom of any element. Hence, for the 
present purpose, an atom may ‘be re- 
garded as the smallest portion of an 
element that can be found in a mole- 
cule of any of its compounds. Alterna- 
tively, an atom is described as the 
smallest particle of an element that 
can enter into chemical combination. 
It is no longer permissible to speak of 
an "atom of a compound,” or of a 
"compound atom,” as Dalton did; the 
ultimate particle of a compound is the 
molecule. If such a molecule -were 
further subdmded it would break up 
into the atoms of its constituent ele- 
ments, and hence would cease to be a 
compound. 


Atoms and. MoleccjijEs 
OF Elements 

1.29. One further point remains to 
be clarified, namely, the distinction 
between the atom and molecule of an 
element. The atom is the smallest 
conceivable particle of an element, as 
well as the smallest portion that can 
take part in chemical combination. 
However, it is not necessarily the 
smallest unit that can normally exist 
as such; it is the latter which is the 
molecule of the element.* Consider, 
for example, the element oxygen, the 
gas which constitutes about one-fifth 
of the air. The atom would be repre- 
sented by the symbol O, but the mole- 
cule, as present in the atmosphere, is 
made up of a combination of two such 
atoms and hence is O 2 . It is true that 
by the use of high temperatures or by 
means of an electrical discharge some 
of the molecules could be split up into 
two atoms, but as soon as normal con- 
ditions were restored the atoms would 
reunite in pairs to form molecules. 
Single atoms of oxygen tend to com- 
bine chemically with other atoms; if 
two atoms of oxygen interact wdth one 
another the result is an oxygen mole- 
cule, but if one atom of oxygen unites 
with two atoms of hydrogen the result 
is a molecule of water. 

1.30. Under ordinary conditions of 
temperature and pressure, most ele- 
ments, at least those which are gases, 
such as oxygen, hydrogen, nitrogen 
and chlorine, form diatomic molecules, 
that is to say, the molecule contains 
t-w'o atoms. There are, however, some 
important elements, often referred to. . 
as the "inert gases of the atmosphere,^ 
for which the atom and the molecule 
are identical. The element helium, for 
example, as it occurs in the atmosphere 
and in certain natural gases, consists of 


of elements m "molficules 41<Smentaires,” and the molecu 

^ mohkules constituantcs.” Molecules of compounds he termed "mo 



10 


SouTcdiook o» 

single atoms and these may equahy 
correctly be descnbed as molecules , 
Thus, helium is said to be a monatomic 
gas The atoms of helium, and of its ' 
related gases neon, argon, etc , are so , 
inert that they will neither unite witli I 
one another nor with the atoms of | 
other elements 

Avoqadro’s Law 
1 31 Beanng m mind the coin^ct 
significance of the term molecule, the 
law of Avogadro states that under the 
same conditions of temperature and 
pressure equal volumes of different 
gases contain equal numbers of mole- 
cules * The density of a gas is defined 
as the weight of a given volume, say 1 
hter, and hence is equal to the weight 
of the molecules contained in that vol- 
ume But, smce for different gases, 
this defiiute volume always mcludes 
the same number of molecules it fol- 
lows that the density of a gas is directly 
proportional to the weight of its indi- 
vidual molecules In the words of 
Avogadro “Setting out from this hy- 
pothesis [as stated above], it is appar- 
ent that we have the means of deter- 
mimng very easily the relative masses 
of the molecules of substances obtain- 
able m the gaseous state for the 
ratios of the masses of the molecules 
are then the same as those of the 
densities oi* the different gases at equaf 
temperature and pressure ” 


Alomic Energy Chap 1 

Determination op / 
Molecular Weights , 
1 32 By the companson of densitits 
it IS thus possible to determine tlie 
weight of one molecular species with 
reference to that of another, and hente, 
for practical purposes, it is desirable to 
choose a uniform basis of reference /'or 
expressing molecular weights That 
proposed by Cannizzaro, and now uni- 
versally adopted, is to use the same 
standard as is employed for atomic 
weights The molecular weight is then 
recorded as the weight of a given mole- 
cule relative to the weight of the oxy- 
gen atom taken as 16 0000 Defined m 
this manner, the molecular weight is 
equal to the sura of the conventional 
atomic weights (§ 1 37) of its constitu- 
ent elements, due allowance being 
made for the number of atoms of each 
present m the molecule 
1 33> There are good reasons for be- 
lieving that the oxygen molecule con- 
sists of two atoms, and so the molecular 
weight of ordinary oxygen is taken as 
32 0000 Hence the molecular weight 
of any substance is the weight of a 
molecule of that substance compared 
with the assumed wei^t of 32 0000 for 
an oxygen molecule It can be readily 
seen, therefore, that m view of Avo- 
gadro’s law, it is possible to wnte for 
any g(w«?ws substance, element or com- 
pound, at the same temperature and 
I pressure, the relationship 


Molecular weight of substance __ Density of substance 
Molecular weight of oxygen ” Density of oxygen 
or, 

Molecular we.ght = of aubsta _ nc _e ^ „ooo, 

^ Density of oxygen 

•Dalton had previously (1808) considered this possibility but had rejected it, ^haps be- 
cause of the confusion between atoms and molecule He wrote ‘ I had a confused id« 
that a given volume of oxygenous gas contains just as many particles as the same volume ot 
hydrogenous But I became convinced that the different gases have not their par 

tides of the same sue fi e , do not occupy equal volumes} ” 



11 


Foundations of the Atomic Theory 


BO that a determination of gaseous 
density is sufficient to yield the mo- 
lecular weight of the substance. It 
may be remarked that the use of ordi- 
nary densities does not give results of 
a high order of accuracy; but by apply- 
ing certain corrections it is possible to 
obtain molecular weights with a con- 
siderable degree of precision.* 

I 

MOLECtTLAB WEIGHTS AND 

Atomic Weights 

1,34. It now remains to be seen how 
the development of a reliable method 
of determining molecular weights pro- 
vided a solution for the atomic weight 
problem. If Dalton had known the 
molecular weight of water to be 18, 
vlth reference to hydrogen as unity, 
it would have been obvious that its for- 
mula could not be HO, as he thought; 
as stated above, this formula implied 
an atomic weight of 8 for oxygen, and 
hence a molecular weight of 1 -f- 8, 
i.e.-, 9, for water. By taking the for- 
mula of water to be H 2 O, and making 
use of the experimental fact that one 
part by weight of hydrogen is united 
with eight parts of oxygen, it is readily 
found that the atomic weight of oxygen 
should be 16. In this event, the mo- 
lecular weight of water would be 2 -k 
16, i.e., 18, as is actually found from 
gas density measurements. Tliis type 
of argument has been used to deter- 
mine the atomic weights of several 
elements. 

1.35, Since the atom is the smallest 
portion of an element that can be pres- 
ent in a molecule, the atomic weight 
must be the smallest weight of the ele- 
ment that can be found in a molecular 
weight of any of its compounds. This 
contention formed the basis of the pro- 
cedure introduced by Cannizzaro for 


the evaluation of atomic weights. Vol- 
atile compounds of a given element 
were prepared and their molecular 
weights derived from gas-density meas- 
urements. The various substances 
were then analyzed so as to find the 
weight of the element present in the 
molecular weight of each compound. 
The smallest weight found in this man- 
ner, or more correctly, the highest com- 
mon divisor of these weights, is the 
atomic weight of the element. 

1.36. Other uses have been made of 
molecular weights in connection with 
the derivation of the atomic weights of 
the elements, but sufficient has been 
stated here to indicate that the proper 
application of Avogadro's law helped 
to remove one of the outstanding diffi- 
culties that faced the chemists of the 
early 1800s. In the latter part of the 
same century methods were developed 
for determining molecular weights 
without resort to gas densities, so 
that nonvolatile solid compounds could 
be utilized in atomic weight studies. 
Further, greatly improved procedures, 
based on the use of chlorides and bro- 
mides, in place of oxides, have been 
employed for obtaining accurate com- 
bining (or equivalent) weights. As a 
result, chemical atomic weights of 
nearly all the elements, as they occur 
on the earth, have been ascertained 
with a considerable degree of accuracy. 
In addition, very precise determina- 
tions of atomic weights have been 
made by means of the mass spectro- 
graph (Chapter VIII). 

1.37, The accompanjdng table gives 
wffiat are believed to be the best values 
of the atomic weights of eighty six 
elements, arranged in alphabetical 
order of their names. The recognized 
symbols for the various elements are 




12 


Sourcebook on Atomic JEnergy 

also given * It should be borne m 
mind that although the data are con- 
sidered to be reliable, some of the re- 
sults may be based on experimental 
determinations containing unsuspected 
errors Consequently, revised hsta of 
atomic weights, which frequently con- 


Chap I 

fain minor corrections, are issued from 
to time, as new and more accurate 
experiments are performed 

PnouT’s Hypothesis 
138 In 1816, when few atomic 
Tveights were yet knmvn, and those 

Atomic Weights 


Element 
Alununutn 
Antimony 
Argon 
Arsenic 
Barium 
Berj Ilium 
Bismuth 
Boron 
Bromine 
Cadmium 
Calcium 
Carbon 
Cerium 
Cesium 
Chlorine 
Chromium 
Cobalt 
Columbiumt 
Copper 
Dysprosium 
Erbium 
Europium 
J Fluorine 
^ Gadolinium 
Gallium 
Germamum 
Gold 
Hafnium 
Helium 
Holtmum 
Hj drogen 
Indium 
Iodine 
Indium 
Iron 

Krypton 

Lanthanum 

Lead 

Lithium 

Lutetium 

Magnesium 

Manganese 

Mercury 


Atomic Atofnte 
Symbol Number TFeJflM 
26 97 
121 76 
39 944 
74 91 
137 36 
9013 
209 00 


A1 

Sb 


Be 

Bi 

B 

Br 

Cd 

Ca 

C 

Ce 

Cs 

Cl 

Cr 

Co 

Cb 

Cu 

Dy 


66 

4 


Er 

Eu 

F 

Gd 

Ga 

Go 

Au 

Hf 

He 

Ho 

H 

In 

I 

Ir 

Fe 

Kr 

La 

Pb 

Li 

Lu 

Mg 

Mn 

Hg 


5 

10 82 

35 

79 916 

43 

U2 41 

20 

4008 

6 

12 010 

53 

14013 

55 

132 91 

17 

35 467 

24 

52 01 

27 

58 94 

41 

92 91 

29 

63 54 

66 

162 46 

63 

167 2 

63 

1520 

9 

19 00 

64 

1569 

31 

69 72 

32 

72 60 

79 

197 2 

72 

178 6 

2 

4003 

67 

164 94 


1 

49 

S3 

77 

26 

36 

57 

82 

3 

71 

12 

25 


114 76 
12692 
193 1 
55 85 
837 
13892 
207 21 
6940 
174 
24-. 
54 93 
200 61 


,T^s,™,Eca»ce of the “atoimc number • 

tS'terSwcuame.^^mCNb) 

{ Alternative name, Wolfram 


Element 
Molybdenum 
Neodymium 
Neon 
Nickel 
Nitrogen 
Osmium 
Oxygen 
Palladium 
Phosphorus 
Platinum 
Potassium 
Praseodymium 
Protactinium 
Radium 
Radon 
Rhenium 
Rhodium 
Rubidium 
Ruthenium 
Samarium 
Scandium 
Selenium 
Sihcon 
Silver 
Sodium 
Strontium 
Sulfur 
Tantalum 
Tellurium 
Terbium 
Thallium 
Thorium 
Thuhum 
Tin 

Titanium 

Tungstent 

Uramum 

Vanadium 

Xenon 

Ytterbium 

Yttrium 

Zme 

, Zirconium 
will be explained 


Atomic 
Symbol Number 
Mo 


Nd 

Ne 

Ni 

N 

Os 

O 

Pd 

P 

Ft 

K 

Pr 

Pa 

Ra 

Rn 

Re 

Kh 

Rb 

Ru 

Sm 

Sc 

Se 

Si 

Ag 

Na 

Sr 

S 

Ta 

Te 

Tb 

T1 

Th 

Tm 

Sn 

Ti 

W 

U 

V 
Xe 
Yb 

Y 
Zn 


10 

28 

7 

76 


15 

78 

19 

59 

01 

88 

86 

75 

45 

37 
44 
62 
21 
34 
14 
47 
11 

38 
16 

73 
52 
65 
81 
90 

69 
50 
22 

74 
92 
23 
54 

70 
39 
30 


Zr 40 
a §5 1 44, 423 


Atomic 
Weight 
95 95 
144 27 
20 183 
58 69 
1400S 
1902 
16 0000 
106 7 
30 93 
19523 
39 096 
140 92 
231 
22605 
222 
18631 
102 91 
85 48 
1017 
150 43 
45 10 
78 96 
28 06 
107 8S0 
22 997 
87 63 
32 066 
180 88 
127 61 
159 2 
204 39 
232 12 
169 4 
118 70 
47 90 
183 92 
238 07 
5095 
1313 
17304 
88 92 
65 38 
9122 


Foundations of the Atomic Theory 


only approximately, the English phy- 
sician William Front thought it pos- 
sible that all atomic weights were in- 
tegral, i.e., whole numbers without 
fractions. All atomic weights, he con- 
sidered, might thus be multiples of that 
of hydrogen. Front then went on to 
say: “If the view we have ventured to 
advance be correct, we may consider 
the prolyh of the ancients to be real- 
ized in hydrogen." * 

1.39. One of the consequences of the 
announcement of Front’s hypothesis of 
the integral nature of atomic weights 
was the stimulus it gave to accurate de- 
terminations of these quantities. WTien 
definite fractional atomic weights, 
such as those of chlorine (35.46) and 
copper. (63.54), were obtained, the hy- 
pothesis fell into disfavor, but in due 
course it came to be realized that there 
was some basis for the idea. If the 


appended table is examined, it will be 
seen that nearly half the elements have 
atomic weights which are within about 
0.1 of a Avhole number. As R. J. Strutt 
(later Lord Rayleigh, 4th Baron) said 
in 1901: “The atomic weights tend to 
approximate to whole numbers far 
more closely than can reasonably be 
accounted for by any accidental coin- 
cidence . . . the chance of any such 
coincidence being the explanation is 
not more than 1 in 1000.” After the 
subject of isotopes has been considered 
in Chapter VIII, it wall be seen that 
both integral and fractional atomic 
weights have an explanation, and that 
Front’s hypothesis, in a modified form, 
has real significance. Even the sug- 
gestion that hydrogen is the primal 
matter or protyle, of which other ele- 
ments are built up, is not completely 
invalid. 


THE FERIODIC SYSTEM 


Classification op the Elements 

1.40. As far back as 1829, J. W. 
Dobereiner had called attention to a 
simple relationship among the atomic 
weights of elements having similar 
properties. The matter attracted the 
interest of other scientists, but their ac- 
tivities were handicapped by the un- 
certainties concerning actual atomic 
weight values. After the publication of 
Cannizzaro’s historic paper in 1858, re- 
liable atomic weights became available 
.and attempts to correlate them wdth the 
physical and chemical properties of the 
elements were increasingly successful. 
In Fr.ance, for example, B. de Chan- 
courtois, in 1862, had arranged the 
elements, in order of increasing atomic 
weight, in the form of a spiral or screwa 
He then found that elements with 


analogous properties occupied related 
positions on the spiral. Quite inde- 
pendently, the English chemist J. A, R. 
Newlands made a similar discovery in 
1865, which he published as the “law 
of octaves.” Newdands stated that if 
the elements are placed in a sequence, 
according to their atomic weights, they 
faU into groups such that the eighth 
element has properties similar to the 
first, the ninth to the second, the tenth 
to the third, and so on, somewhat Uke 
a series of octaves in music. Although 
the scheme had some merit, Newlands 
carried the octave rule too far. This 
fact, combined with his use of incor- 
rect atomic weights in some instances 
and his failure to realize that elements 
might exist which had not yet been 
identified, resulted in some highly im- 





14 


Sourcebook on Atomic Energy Chap I 


probable associations Thus, iron found 
itself classified with sulfur, and gold 
ivith iodine, associations which no 
chemist could accept 

The Periodic Law 

1 41 In 1869, the Russian scientist 
D I Mendelyeev* published a short 
note On the Eelahonships of the Prop~ 
erlies of the Elements to their Atomic 
Weights, which he subsequently elabo- 
rated, in 1871, m the form of a lengthy 
paper on The Periodic Regularities of 
the Chemical Elements Although Lo- 
thar Meyer m Germany had indicated 
in 1864, and again in 1869, that certain 
properties of the elements were a peri- 
odic function of their atomic weights, 
it IS the Russian chemist who is re- 
garded as the effective ongmator of the 
periodic law, and of the method of clas- 
sifying the elements based on this law 
It was already apparent, Mendelyeev 
said, "during the period 1860-1870 
that relations between atomic 
weights of analogous elements were 
governed by some general and simple 
law When I arranged the ele- 
ments according to the magnitude of 
their atomic weights, beginning ivith 
the smallest, it became evident that 
there exists a kind of periodicity m 
their properties I designate by the 
name periodic law the mutual relations 
between the properties of the elements 
and their atomic weights, these re- 
lations are applicable to all the ele- 
ments and have the nature of a peri- 
odic function " 

1.42 The success of Mendelyeev’s 
arrangement of the elements lay m his 
emphasis on the repetition of physical 
and chemical properties at definite 

* The Russian name has been transliterated 
taken from Webster's New Intemaiional 

t An account of Mendelyeev’s work, bebevi 
the London Chemical News m December, 1875 
m 1879-80 

} These are the paun argon and potassiuim < 
which the atomic weight dmerences are small 


intervals Where the periodic prop- 
erties appeared to break down, he 
boldly proclaimed that in some m 
stances the accepted atomic weights 
were grossly in error, wble in others 
allowance must be made for elements 
as yet undiscovered It is m the lat- 
ter connection that the periodic law 
achieved its most striking successes 
By considering the properties of known 
elements surrounding the gaps left for 
apparently missing elements, Men- 
delyeev predicted the behavior of the 
latter in great detail In three cases, 
m particular, the discovery of the actual 
elements, gallium in 1875, scandium 
in 1879 and germamum in 1886, pro- 
vided a bnlliant vindication of these 
predictions It was, in fact, not until 
1875, when the French chemist L de 
Boisbaudran identified, in zme blende 
from the Pyrenees, a hitherto unknown 
element, which he called gallium, that 
the periodic law began to attract gen- 
eral interest t 

1.43. Although some of Mendel- 
yeev's prognostications were subse- 
quently found to be incorrect, and 
certain features of his onginal periodic 
deification have had to be amended, 
the fundamental principles of his law 
reraam unchallenged It is now ac- 
cepted as one of the cardinal truths of 
nature, and a close connection has been 
estabbshed between the positions of 
the elements in the periodic arrange- 
ment and the mtemal structure of 
their atoms 

1 44 A modem form of the penodic 
table, which mcludes all the known 
elements arranged, with some minor 
exceptions,^ m the order of increasing 
atomic weights, is appended The/ 
m many different ways the one given here is 
nary Second Bditiom 1941 
d to be the first in English, was published in 
, his 1871 paper was translated in this journal 

obalt and nickel, and tellunum and Iodine for 







16 


iS(mrce6ool on Atomic Energy 


eight elements whose B3rmbol3 are in 
parentheses appear to be too unstable 
to exist in nature to any appreciable 
extent, they have, however, been pro- 
duced m recent years by the disinte- 
gration and transmutation of other 
elements The ordinal number of each 
element in the senes, referred to as the 
aComtc number {§ 4 23), is given m each 
case 

1 46 The table is seen to consist of 
a number of honzontal Imes, called 
■periods, containing 2, 8, 8, 18, 18, 32 
and 12 (incomplete) elements, respec- 
tively * In each period there is defi- 
nite and characteristic gradation of 
chemical and physical properties, from 
one element to the next In some 
places the gradation is quite marked, 
e g , Al, Si, P, S, Cl, A, but at other 
points, eg, Cr, Mn, Fe, Co, Ni, Cu, 
Zn, It 15 relatively small These facts 
ha\e been explained m terms of the 
structures of the atoms of the respec- 
tive elements 

1 46 The vertical columns into 
which the table is divided are called 
groups, most of the'« groups consist of 
A and B subgroups, viz , lA, IB, IIA, 
IIB, etc Similanties of a minor char- 
acter exist between the members of an 
A subgroup on the one hand, and those 
of the corresponding B subgroup on 
the other hand In each subgroup the 
elements have analogous properties, 
although there is a steady but gradual 
variation within creasmgatomic weight 
It IS this repetition of physical and 
chemical cbaractenstics, occurring at 
regular intervals, that represents the 
periodicity to which Mendelyeev, and 
others, called attention 

1 47 The presence of Group 0, con- 
sisting of the “inert gases," is of par- 
ticular interest None of the elements 


Chap I 

of this group had been identified, at 
least on the earth, until 1895, hence, 
the early groups in the periodic table 
were numbered from I to VIII When 
the mert gaees of the atmosphere were 
discovered it was soon seen that they 
formed a group between VIIB and lA, 
but, m order to avoid a complete re- 
numbenng, the symbol 0 (zero) was 
assigned to the new group This sym- 
bol is especially appropnate because of 
the highly mert nature of the elements 
concerned 

Lanthanide and Actinide Series 

1 48 There are numerous other im- 
portant features of the periodic table, 
but the discussion given here will be 
restricted to one of particular interest 
In Group IIIA, Period 6, there ap- 
pears, m place of a single element, a 
senes of fourteen elements with atomic 
(ordinal) numbers from 57 to 71, in- 
clusive, the details of which are re- 
corded below the mam table These 
elements, called the ktntkamde senes, 
after the name of its first member (lan- 
thanum), are more familiarly known 
as the Tare-earih senes They have 
properties which are so closely related 
that their separation from one another 
has long presented a challenge to chem- 
ists 

1 49, In view of the existence of the 
lanthanide senes, there has been much 
speculation concemmg the possibility 
of the occurrence of an analogous ac- 
tinide senes, beginning with the ele- 
ment actinium, atomic number 89 In 
the periodic tables to be found m books 
and papers pubhshed before 1945, and 
even later, the four elements of this 
possible senes, whose properties were 
generally known at the time, namelj^ 
actinium, thorium, protactinium and 


• It was the occurrence of the second and thud periods of eight elements, of which s^en 
were known at the time, that led Newlands to propose his ‘ law of octaves ” Since the subse- 
quent periods are considerably longer it is obviom that the “law ’ must then break down 



17 


Foundations of the Atomic Theory 


uraniunn, are placed in Groups III A, 
IV A, V A and VI A. In other words, 
prior to 1945, naost chemists would 
have doubted the existence of an acti- 
nide series; the feeling was that Period 
7 would behave more hlce Period 5 
than like Period 6. However, infor- 
mation obtained since 1939 has thrown 
an entirely new light on the situation 
(see Chapter XV). A detailed study of 
the chemical properties of the new 
“artificial” elements neptunium (Np, 


93), plutonium (Pu, 94), americium 
(Am, 95), curium (Cm, 96) and ber- 
kelium (Bk, 97), and a reinvestigation 
of those of uranium (92), has shown 
clearly that these elements have prop- 
erties which would make them mem- 
bers of a series similar to the lantha- 
nide series. The same will probably 
prove to be time for the element cal- 
ifornium (Cf, 98), the discovery of 
Avhich was announced early in 1950. 


THE SIZES AND WEIGHTS OF ATOMS 


Atomic Weights and the 
Reality of Atoms 

1.60. So far, the atomic concept has 
been presented here purely as a Avork- 
ing theorjf, without any definite proof 
that atoms actually exist. B 3 ’- assum- 
ing that compounds are composed of 
molecules, Avhich are themselves built 
up from atoms of various elements, it 
has been possible to ascribe so-called 
atomic Avcights to these elements. The 
fact that the arrangement of the ele- 
ments in order of increasing atomic 
weight brings out a striking periodicity 
of characteristic properties, suggests 
tlvat these Aveights do have significance. 
The results thus provide some support 
for the theorj' that all matter is con- 
structed ultimatelj’- of atoms. How- 
ever, if information could be obtained 
rom A'arious sources concerning the 
izos and actual weights, as distinct 
rom the relative %Anights, of atoms, a 
cneral agreement among the results 
light serAn as a more conAuncing argu- 
lent for the atomic theory. 

Moleculab Size: 

Early Estimates 

1.61. The first reasonably accurate 
timate of molecular size was pub- 


lished by the English physicist Thomas 
Young, in an essay on Cohesion/ Avrit- 
ten in 1816 for the Supplement of the 
Encyclopaedia Britannica. In this ar- 
ticle, he said: “Within certain limits of 
accuracj’-, aa'c may obtain something 
hke a conjectural estimate of the 
mutual distance of the particles of va- 
pours, and even of the actual magnitude 
of the elementarj’’ atoms of liquids, as 
supposed to be nearly in contact with 
each other; for if the distance, at AA^hich 
the force of cohesion begins, is con- 
stant at the same temperature, and if 
the particles of steam are condensed 
Avhen they approach within this dis- 
tance, it follows that at 60° of F. the 
distance of particles of pure aqueous 
vapour is about the 250 millionth of 
an inch.” From this result and a com- 
parison of the densities of hquid and 
vapor, Young concluded that the di- 
ameter of a water molecule was about 
a billionth, i.e., 10-«, of an inch. Con- 
sidering the approximate nature of the 
calculation and the verj”- small magni- 
tudes invohmd, this result is remark- 
nblj”^ good, being onlj’’ about ten times 
smaller than the value now accepted. 

1.62. Thomas Young’s estimate of 
molecular size was based on intelligent 
guessing, but further developments in 



18 


Sourcehoolo on 

physical theory were necessary before 
substantial progress could be made 
One of these was related to the be- 
havior of gases The fact that gases 
exert a pressure or “spring/^ as Robert 
Boyle called it, had been explained by 
the kinetic theory According to this 
theory the molecules of a gas are as- 
sumed to be constantly m motion, 
frequently striking one another and the 
walls of the containing vessel, and so 
continually changing their directions 
Making use of this relatively simple 
concept, mathematicians and physi- 
cists, notably R Clausius m Germany 
and J C Maxwell in England, in the 
period between 1850 and 1860, were 
able to denve a number of equations 
relating certain measurable properties 
of a gas to the characteristics of the 
individual molecules One of these 
equations showed how the viscosity, or 
resistance to flow, of a gas depended on 
the sise of the molecules and the num- 
ber present m unit volume However, 
since neither of the latter quantities 
was known the relationship to the 
viscosity, which could be determined 
experimentally, appeared to have no 
practical value, since no solution can I 
be obtained for a single equation with 
two unknown quantities i 

1 63 The dilemma was solved m a j 
simple, if approximate manner by the 
German jentjist. J Losrhmidt in J5f*5 
He pointed out that if molecules could 
be regarded as spherical m shape, and 
if, further, it was supposed that m the 
hquid state these molecular spheres 
were packed as closely as possible, an- 
other equation could be readily derived 
relating these same two quantities to 
the density of the liquid Hence, if 
there are known the viscosity of a 
particular gas and the density of the 


Atomic Energy Chap i 

hquid which is formed when the gas js 
compressed and cooled, the two equa^ 
tions permit the size of the given mole- 
cule and the number present m a unit 
volume to be calculated 

1 54 Applying this procedure to ni- 
trogen, oxygen and carbon dioxide, 
Ij<fflchmidt found these molecules to be 
slightly more than one ten-millionth of 
a centimeter i e , 10“’cm , m diameter, 
a value now known to be too large 
by a factor of about five, but, neverthe- 
less, of the correct order of magmtude 
In addition, the calculations showed 
that m each case there were present, 
under ordinary conditions of temper- 
ature and pressure, about two bilhon 
billion, 1 e , 2 X 10'®, individual mole- 
cules m one cubic centimeter (1 cc), 
a figure which is some fourteen times 
too small * The eight of 1 cc of 
oxygen gas, for example, is known, and 
consequently the weight of a single 
oxygen molecule could be calculated 
The weight of an atom w ould then be 
one-half of this quantity In spite of 
their approximate nature, partly due 
to the use of inaccurate viscosity data 
and partly because of the assumption 
that a liquid consists of close-packed 
spheres, Loschmidt’s results are im- 
portant, for they represent the first 
attempt, based on sound theoretical 
principles to estimate the properties 

1 66 In 1870, the eminent Scottish 
physicist and inventor, William Thom- 
son, later Lord Kelvin, reviewed a 
number of methods for determimng 
molecular size, and concluded that 
they all led to values of the same order, 
namely, about 10“® cm for the diam- 
eter of a molecule In a lecture de- 
livered at the Royal Institution, Lon- 
don, m 1881 he tried to convey some 


* According to Avogadro’s law the number of molecules m 1 cc of gas should be the same, 
at a given temperature and pressure, for dU gases Within the limits of their accuracy, 
Loschmidt's results confirmed the law 



idea of the extreme smallness of atoms 
and molecules as follows: “To form 
some conception [of molecular size] 
. , . imagine a globe of water as large 
as a [spherical] football . . - , say 16 
centimetres in diameter, to be magni- 
fied up to the size of the earth, each 
constituent molecule being magnified 
in the same proportion. The magnified 
structure would be more coarse-grained 
tlrnn a heap of small shot but probably 
less coarse-grained than a heap of foot- 
balls.” 


The Avogadro Nttmber 
1.66. Before proceeding to a 


dis- 


cussion of more recent work dealing 
with molecular properties, reference 
must be made to an incidental matter. 
By Avogadro’s law, the number of in- 
diiddual molecules in a given volume 
of (ideal) gas is independent of the 
chemical nature of the gas. For pur- 
poses of record any convenient volume 
may be chosen, but there is a particular 
voliune that has special significance. 

If the molecular weight of any sub- 
stance is expressed in grams, the re- 
sulting quantity is knowm as a gram 
vwlcaihr weight, a gram molecule or, 
more briefly, as a mole of the substance. 
Tlius,. 2.016 grams of hydrogen, 32.000 
grams of oxj’’gen and 28.020 grams 
of nitrogen, each represent one mole 
of the respective substances. Experi- 
ments with a large number of gases 
have showm, in accordance with Avo- 
gadro’s law, that, after correcting for 
departure from ideal behavior (§ 1.33, 
footnote), one mole of any gas always 
has a volume of 22.414 liters at a tem- 
perature of 0°C and a pressure of 1 
atmosphere. This is known as the 
gaseous molar volume at standard tem- 
porahire and pressure, and the number 
of jndividual molecules present in this , 

roust contain the 


Foundations of the Atomic Theory 19 

volume, which is the same for all gases, 
is called the Avogadro number or Avo- 
gadro’s constant. 

1.67. Since the molar volume con- 
tains one mole, the Avogadro number 
is the number of individual molecules 
in one gram molecule.* Hence, if the 
molecular weight of any substance, 
element or compound, is divided by 
the Avogadro number, the result is the 
w^eight expressed in grams of a single 
molecule of that substance. Similarly, 
the weight in grams of a single atom of 
any element is obtained upon dividing 
its atomic weight by the Avogadro 
constant. 

1.68. One of the most notable stud- 
ies relating to molecules was under- 
taken in France by J. Perrin, beginning 
about 1908. Some eighty years earlier, 
the English botanist Robert Brovra 
had noticed that when microscopic pol- 
len grains were suspended in water, 
they exhibited continual and haphaz- 
ard motion in all directions. In fact, 
their behavior was, on a large scale, ex- 
actly what would have been expected 
from molecules if they behaved in 
accordance with the kinetic theory 
(§ 1.62). The phenomenon, which has 
been obseived with small suspended 
particles of many kinds, is called the 
Brownian moveMent, the motion being 
attributed to the continuous bombard- 
ment of the particles by the molecules 
of the medium in which they are sus- 
pended. Thus, the movement of the 
particles, as seen in the microscope, 
represents in a sense a highly magnified 
picture of the motion of the invisible 
molecules which surround them. Per- 
rin made a series of measurements on 
various tjTDes of suspended particles, 
and by assuming that they behaved 
just like molecules obeying the equa- 
tions derived from the kinetic theory 


tivo of r • contain the same number of individual molecules irrespec- 



20 


Sourcebook on Aiormc Energy Chap i 


of gases, he was able to calculate the 
Avogadro number 

1 69 In other experiments on the 
motion of suspended particles, Pemn 
made use of an equation first derived 
by A Einstein in 1905 By combimng 
this ivith other equations further re- 
lationships were obtained which per- 
mitted independent estimates to be 
made of the number of molecules con 
tamed in a given volume of gas The 
striking fact that emerged from this 
work was that the value of the Avo- 
gadro number was alw ays the same — 
about 6 X 10*^ — within the limits of 
experimental error irrespective of the 
tipe of measurement upon which it 
was based Further, the value was in 
excellent agreement with that derived 
from more refined calculations of the 
type first made by Loschratdt, utilizing 
the properties of gases The fact that 
observations of such entirely different 
types gave virtually identical results 
was of the greatest significance Apart 
from yielding information concerning 
the Avogadro number the work of 
Pemn has been regarded as pro\ iding 
some of the most convincing evidence 
for the real existence of molecules 

1 60 Several other procedures for 
evaluating the Avogadro constant, 
rangmg m scope from radioactivity to 
the blue color of the sky, have been 
developed Two of these give results of ' 
special accuracy, the first is based on , 
measurement of the charge earned by 
an electron (§ 2 41), and the second ' 
iniolves X-ray studies with crystals | 
The value of the Avogadro number 
thus obtained is 6 023 X 10"*, and this I 
IS the number of individual molecules i 
in a gram molecular weight, i e , in a 
mole, of any substance 

Atoms in Gas, Solid and Liquid 

1 61 Under ordinary atmospheric 
conditions, 1 cc of a gas, irrespective 


of its nature, contains about 2 7 X 10 ’ 
molecules Gaseous molecules are usu 
ally made up of from 1 to 10, or per 
haps more, atoms and so the volume 
of gas specified includes, on an average 
a total of something like 10*“ atoms 
In certain atomic studies, some ot 
which will be referred to later m thu 
book, it IS necessary to produce whai 
IS known as a "high vacuum," by 
pumping as much as possible of the 
gas from the containing vessels How 
ever, even m the best vacuum normally 
attainable, with the pressure reduced 
to one billionth (10“*) of an atmos- 
phere, or less, 1 cc of gas, at normal 
temperature, still contains more than 
ten billion, i e , more than 10‘® mole- 
cules 

1 62 Liquids and sohds being more 
highly condensed than gases, contain 
even more atoms and molecules per 
unit volume As distinct from the be- 
havior of gases the number of mole- 
cules now depends on the nature of the 
substance It is determmed, essen 
tially, by the ratio of the density of the 
solid or liquid to that of the same 
material m tlie form of gas or vapor 
But as a rough approximation, it may 
be stated that a solid or liquid contains 
about one thousand times as many 
atoms as an equal volume of gas at 
normal pressure Consequently under 
ordinary conditions there are some- 
thing hke 10** atoms in 1 cc of hquid 
or sohd material 

1 63 The number of molecules in a 
specified weight of any material, gase- 
ous, liquid or sohd, can be calculated 
m the following manner The weight 
m grams is first divided by the molec- 
ular weight, to give the number of 
moles piesent Upon multiplication of 
this result by the Avogadro number 
1 e , 6 02 X 10**, which is the number 
of molecules m 1 mole, there is ob- 
tained the total number of individual 



rnoleculss in the material. If the latter 
is an clement, division of th? weight by 
the atomic weight and multiplication 
by the Avogadro number gives, corre- 
spondingly, the number of atoms pres- 
ent. 

Weights and Sizes of 

Atoms and Modechles 

1,64. As already stated, the weight 
in grams of a single atom or molecule 
can be determined by dividing the 
respective atomic or molecular weight 
by the Avogadro number. Thus, the 
weight of the lightest atom, hydrogen, 
is found to be 1.67 X 10“=^ gram, while 
that of the heaviest, naturally occur- 
ring element, uranium, is 3.95 X 10"“ 
gmm.* Special balances, designed for 


weighing small quantities (§ 15.16), 
can detect a weight as small as 10“^ 
gram. Such a minute speck of matter, 
say of uranium, would be invisible to 
the naked eye, but it would, neverthe- 
less, contain more than 10'^ atoms. 

1.65. Now that the Avogadro con- 
stant, and hence the number of mole- 
cules in 1 cc. of ga.s, may be regarded 
as knowi, use may be made of .the 
kinetic theoiy equations, referred to 
earlier, to derive molecular diameters 
from such mc.asuiements as the ids- 
cosity, diffusion or he.at conductivity 
of gases. Since the number of atoms 
in the molecule is usually knonm, an 
estimate ma 3 '’ be made of the diametem 
of some of the lighter atoms. In this 
waj", the diameter of a hi'drogen atom, 
the smallest atom of all, is found to be 
1.35 X 10“® cm., that of helium 2.2 X 
10"'' cm., and of nitrogen and oxj'gen 
about 1.8 X 10"^ cra.t ' Thus, the lighter 


Foundations of the Atomic Theory 21 

atoms, and molecules containing a rela- 
tively few atoms, have diameters of the 
order of 10"® cm. For atoms, at least, 
which may be regarded as spherical 
in shape, this also represents the mag- 
nitude of atomic radii. 

1.66. An approximate estimate of 
molecular and atomic radii can be 
made by utilizing Loschmidt’s assump- 
tion that a liquid or, better, a solid 
may be treated as an arrangement of 
closely-packed spherical molecules (or 
atoms) . The molecular weight of water, 
for example, is 18, and hence 18 grams 
of water, which occupy about 18 cc. 
in the liquid state, contain 6 X 10“, 
the Avogadro number, of molecules. 
If the water molecules were cubic in 
shape, so that they packed together 
without any free space, the volume of 
a single molecule would be 18 divided 
by 6 X 10“,i.e., 3 X 10"“ cc. Assuming 
a spherical shape, the volume would be 


somewhat less, saj' about 2 X 10"“ cc. 
The volume of a sphere of radius r is 
4irr®/3, where tt has its usual value of 
3.14; consequently it can be readily 
calculated that if the water molecule 
were spherical, its radius would be 
about 1.7 X 10"® cm. It can be seen 
that this simple method gives results 
of the correct order of magnitude, and 
provides an approximate indication of 
molecular and atomic dimensions. 

1.67. Individual atoms thus are so 
small that thej’^ cannot be detected, 
even in the most powerful electron 
microscopes, -which give a magnifica- 
tion of about 100,000. It is possible 
that some large naturally occurring 
molecules, particularly those which are 
protein-like in character, can be ren- 

con- 
„ of a 
ay they are packed 

vuuus luuseiy pacsea rmgnt mve a SQUa Ot ’ ' ‘ 

. . ^vry tiKhlly mcked. 

t riK-c fipircs arc probably all about 0.3 X 10"* cm. larger than the true atomic diameters 



^ l^wer^densIS E 


atomic diameters 

l^-o distance to which 



22 


(Sourccboofc on 


dered visible m this manner, but each 
of these complex molecules consists of 
thousands of atoms The smallest 
speck of matter which might be ex- 
pected to be visible m a good, optical 
microscope would contain something 
like a billion (10’) atoms! 

1 68 In recent j ears three methods, 
in particular, have been used to deter- 
mine the sizes of atoms and molecules 
For solids the diffraction of X-rays 
(§ 2 88) has been employed, and for 
gases application has been made of the 
diffraction of electrons (§3 42), and 
also of the so-called “band” spiectra of 
molecules For purposes of reference, 
and as a matter of general interest, the 


Approximate Atomic Radii 



Atomic 


Aiomic 

Slmeni 

Radma 

Elmint 

Ttodiua 

Hydrogen 

0 53 A 

Aluminum 

145A 

Oxygen 

0 74 

Magnesium 

16 

Carbon 

0 77 

Lead 

175 

Arsenic 

12 

Sodium 

10 

Tin 

14 

Polassmm 

235 


Aiormc Energy Chap } 

approximate atomic radii of a numbei 
of the more familiar elements are 
quoted here For convenience, the le- 
sults are expressed m Angstrom unite 
where 1 Angstrom, represented by the 
symbol A , is equal to 1(H cm 
1 69. It is a remarkable achievement 
that, in spite of their almost infinj 
tesimal smallness, atoms have been 
weighed and measured The results 
have been obtained indirectly, it is 
true, but they are believed to be just 
as certain as if each individual atom 
had been handled Still more wonder 
ful m the fact that methods have been 
found for prying mto the very mtenor 
of the atom and of studying its de- 
tailed structure Althou^ a great 
deal still remains to be discovered in 
this field, striking progress has already 
been made Much of the information 
has stemmed from studies on the pas- 
sage of electricity through gases at 
low pressures, a subject which will be 
considered in the next chapter 



Constituents of the Atom Chwptev II 


THE NATURE 0 

Positive and Negative 
Electricity 

2.1. As with so manj’- modern ideas, 
the origin of the study of electricity 
may be traced to the Greeks. The 
philosophers of ancient Greece were 
inclined to be thinkers rather than ex- 
perimenters, but they did. observe, as 
far back as 600 B.C., that when a 
piece of amber is rubbed, for exam- 
ple, with fur or cloth, it acquires the 
property of attracting to itself light 
particles, such as feathers and wool. 
This phenomenon was studied by Wil- 
liam Gilbert, personal physician to 
Queen Elizabeth, in the latter half of 
the sixteenth century, and for it he 
proposed the name ehctricity, after the 
Greek word elekiron, meaning amber. 
Gilbert also noticed that other sub- 
stances besides amber, such as glass 
and some gems, become electrified 
when rubbed, so that they are then 
able to attract light particles. 

2.2. Little progress Avas made for over 
a hundred years until 1733 w'hen C. F. 
DuFay in France found that although 
sealing wax rubbed wdth cat’s fur and 
a glass rod rubbed with silk both be- 
come electrified, there is a difference 
in the electrification they acquire. 
Tlius, an electrified body which is 
attracted by the sealing Avax is 
strongly repelled by the glass, and vice 
versa. The two kinds of electricity 
Averc called vitrcom (glass) and resinous 
(sealing wax). But it was the remark- 


’ ELECTRICITY 

able American philosopher and states- 
man Benjamin Franklin, Avho, in 1747, 
proposed the terms ‘positive and nega- 
tive electricity, Avhich are still in general 
use. In the middle of the eighteenth 
century electrification Avas considered 
to be due to a “fluid,” and Franklin 
thought that Avhen glass was rubbed 
Avith the dry hand, some of the electric 
fluid passed from the hand to the glass. 
The latter thus haAung an excess, or 
“plus,” of electric fluid was said to be 
electrifled positively, w^hile the hand, 
having a deficit, or “minus,” of the 
fluid was regarded as having a negative 
charge. 

2.3. Franklin was apparently una- 
ware of DuFay’s classification of Aatre- 
ous and resinous electricities, but others 
soon realized that the former was 
equivalent to Franklin's positive and 
the latter to his negative electricity. 
Thus, while glass becomes positively 
charged, sealing wax acquires a nega- 
tive charge wheh rubbed. The obser- 
vations made by DuFay relating to the 
attraction and repulsion of charged 
bodies are readily explained if it is 
supposed that imlike charges attract, 
AA’hereas like charges repel one another. 
The positively charged glass attracts 
the negatively charged sealing wax, 
but repels another posithmly charged 
glass rod. 

2.4. Actually, Franklin had no valid 
grounds, as he seemed later to realize, 
for believing that glass acquires an 



24 Sourcebook on 

exces<5 of electricity when rubbed Con- 1 
sequently, bis use of the terms positive | 
and negative were really arbitrary j 
Nevertheless, they are used today in ! 
the same sense as when they were in- | 
troduced about two hundred years ago 
Any electriBed body which repels, or 
IS repelled by, electrified glass, or at- 
tracts, or IS attracted by, electrified 
sealing uax is said to be positively 
electrified or to carry a positive electric 
charge Similarly, an electrified body 
IS regarded as having a negative charge 
when It attracts electrified glass and 
repels electrified sealing wax It will 
be seen m § 2 53 that it would have 
simplified many things if Franklin had 
concluded, as he nught well ha\ e done 
that glass became negatively electnfied 
when rubbed Unfortunately, he did 
not do so, and the study of elcctncity 
has become so thoroughly imbued with 
these particular associations of positne 
and negative charges that it would 
now be virtually impossible to make 
any change, no matter how convenient 
such a change might prove to be 

Static and Dynamic ELEcrnicmr 
2 6 The electrical phenomena 
studied by Gilbert, DuFay, FranUm 
and others have become known as fric- 
tional or static electricity — because of 
its mode of production — to distinguish 
it from the so-called dynamic elec- 
tricity, discovered at the end of the 
eighteenth century In 1780, the anat- 
omist Luigi Galvam, m Italy, had 
noticed that when one of the nerves of 
a freshly killed frog was touched with 
n metal scalpel while an electric spark 
was being produced on a nearby fnc- 
tional machine, the muscles of the frog 
twitched Later, while investigating 
the phenomenon, which he attnbuted 
to “animal electricity," he found that 
similar effects could be produced by 
making contact between two pieces of 


Atomic Energy Chap 11 

metal, one of which was placed touch 
ing a muscle, and the other a nerve of 
the frog 

2 6 The “animal" nature of the 
electricity was doubted by a contempo- 
rary Italian physicist Alessandro Volta, 
who suggested that the essential factor 
m the production of the effects ob- 
served was the presence of two metals 
He proved the point m 1796 by shoe- 
ing that electncity could be generated 
by means of pieces of two different 
metals, such as zmc and silver, sepa 
rated by wet pasteboard or leather 
A system of this tj^pe subsequently 
became knoivn as a galvanic or voltaic 
cell, in honor of Galvam and Volta, 
respectively 

POTEVTIAL AND CDBRENT 

2.7. The kind of electricity produced 
by a cell — called gahamc or voltaic 
clectncity—appeared at first to be 
different from the frictional electricity 
which resulted from nibbing a non 
mctalbc substance The former bad 
the property of flownng along a metal 
wire, whereas the htter appeared to be 
confined to a particular body, so that 
the terms dynamic and static were 
employed, as stated above HonTver, 
after various expenmenters, during the 
early years of the nineteenth century 
had shown that identical effects could 
be produced by both static and dy 
namic electncity, the famous English 
scientist Michael Faraday, m 1833 
explained the apparent difference 

2 B In 1776, Henry Cavendish had 
suggested that two electrical factors^ 
namely, “quantity" and “intensity, 
must be distinguished For the pur 
pose of analogy, electncity may be 
compared wnth the flow of water m & 
waterfall The intensity of electricity, 
referred to as the potential or lollagi 
since it IS usually measured in voU 
umts, IS equivalent to the height of the 

s 



25 


Consiiiuenis of the Atom 


foil; while the quantity of electricity, 
sometimes called the charge, is similar 
to the amount of water in the fall. 
One waterfall may be very high but 
contain the merest trickle of water, 
whereas another may consist of a large 
volume of water falling through a rela- 
tively small height. So it is with elec- 
tricity. Faraday showed that in static 
electricity the potential or voltage is 
high, but the charge or quantity is 
small; in dynamic electricity, however, 
the situation is reversed, compara- 
tively speaking, the voltage being 
smaller while the quantity is larger. 
The energy available at the bottom of 
a waterfall is determined by the prod- 
uct of the height of the fall and the 
quantitj’- of water falling. A similar 
rule applies to electricity: the electrical 
encrgj' is calculated by multipl 5 dng 
together the potential and the charge. 

2.9. When two bodies, one of which 
is charged positively and the other 
negatively, are connected together, by 
a metal rod or wire for example, a flow 
of electricity, referred to as an electric 
crirrent, will be produced. Even if the 
connecting vdre is not used, and the 
potentials of the charged bodies — one 
positive and one negative — are high 
enough, so that there is a large ’potential 
difference between them, electricity 
will flow from one body to another in 
the form of an electrical discharge, 
.such as a spark or a series of sparks. 
Lightning is a discharge of this tj-pe. 

2.10. Since the quantity of electric- 
ity on a body charged statically, 
e.g., by friction, is small, the current 
.strength, i.c,, the rate at which the 
charge flow.?, usually measured in am- 
peres, will be small. If higher currents 
arc required, at a sacrifice of potential, 
a form of voltaic or galvanic cell is 


employed. By combining a large m^- 
ber of such cells in series, it is possible 
to step up the potential, to something 
of the order of a thousand volts or 
more, while maintaining a moderate 
current strength. A similar result may 
be achieved by using a dynamo, which 
is a machine for converting mechanical 
into electrical energy (§ 3.2). 

2.11. By convention, the positive 
direction of flow of electric current is 
taken to be from the positively charged 
body to the one carrying the negative 
charge. The terms positive and nega- 
tive as used here correspond exactly 
to their definitions by Franklin. Ho\y- 
ever, it is no longer necessary to use the 
primitive tests of attraction and re- 
pulsion of charged bodies. When an 
electric current passes through a wire, 
disturbances occur in its neighborhood 
which influence a magnet in a definite 
manner,* depending on the direction 
of flow. Similarly, chemical effects ob- 
served w'hen electricity passes through 
a solution are characteristic of the 
current direction. Thus, magnetic or 
chemical (electrolytic) tests readily 
serve to indicate the direction of cur- 
rent flow. Every source of electric 
current, w'hether it be a single cell, a 
group of cells or a dynamo, consists of 
two poles, plates or electrodes, as they 
are variously termed. A positive sign 
is allocated to one and a negative sign 
to the other, so that the direction of 
current flow is from positive to nega- 
tive. 

Alternating Current 

2.12. Hitherto it has been tacitly 
assumed 'that the floAV of electricity is 

I unidirectional; this is known as direct 
current or DC. However, several de- 
vices in common use, such as a dynamo 


euwnt f wcmity of a wire carrjing ai 

f TcicTS, m general, to a region or space throughout which 
tiarucular hnd of force, e.g., magnetic, electric, gravitational, etc., h being SS 



26 


Sourcebook on Atomic Energy Chap 11 

(without a commutator) , an induction decreased, very simply by means of th? 
coil and a vacuum-tube oscillator, pro- instrument kno^vn as a transformer 
duce alternating current or AC, i e , a As will be seen in Chapter IX, such 
current uhose direction is continually high voltage currents, of relatively 
reversed at definite mtervals Each high frequency, have important uses 
pole thus becomes alternately positive in atomic studies It is true that in the 
and negative, and has no specific sign transformer the current strength is 
With a dynamo the frequency of the dimimshed proportionately as the volt- 
altemations depends on the rate of age is increased, but this is usually of 
rotation of the armature, and is usu- no significance By means of a recti 
ally moderately low, for example, sixty fier, alternating current can be con 
cycles per second for ordinary house verted into direct current Vanom 
current in the United States By types of rectifying devices are avail 
means of properly designed vacuum- able, as, for example, mechanical 
tube oscillators, alternating current of vacuum-tube, copper-copper oxide and 
various frequencies, from relatively selenium rectifiers In order to obtain 
low to very high, e g , radio and radar, direct current at high potentials, the 
can be obtained common procedure is to produce alter 

213 The ad\antage of alternating natmg current m a convenient manner 
current is that its voltage, or potential step up its potential by means of a 
difference, can be greatly increased, or transformer, and then rectify 

PASSAGE OF ELECTRICITY THROUGH GASES 

Ei/Ectrical Discharge apparently much easier to do so if the 

AT Low pREsatTRES gas pressure is decreased The voltage 

2 14 In 1705, F Hauksbee, in Eng- adequate to produce the discharge at 

land, found that there was an emission reduced pressures, although stifi high 
of light when amber was electrified by ^ considerably lo\\er than the spartog 
rubbing m a closed vessel, in v hicli the potential at atmosphenc pressure 
pressure of the air had been reduced low-pressure discharge is less 

by a pump At ordinary atmospheric ''loJent than a spark, and is associated 
pressure the light was not observed with various luminous phenomena 
A related effect was noted by William familiar neon signs widelv used m 
Watson m 1752, he found that a dis- advertising provide an excellent illus- 
charge of static electncity w ould pass tration of the effect of electrical dis- 
much more readily through a gas at charge in a gas at reduced pressure 
low pressure than at atmosphenc pies ^ reason why electnci y 

sure The passage of the dischar^ w as travel more readily through a gas 
accompanied by a lummosity m tbe fmv pressure is, bnefly, somew a 

contammg vessel Although it is pos- follows The passage of electnci y 

sible, by means of sufficiently hi^ from one point to another requires the 
potential, which may be either alter- presence of electrically charged par 
natmg or umdirectional, to pass a dis- tides, frequently atoms or molecules 
charge in, the form of a spark throu^ to which the general name of ions is 
a gas at atmosphenc pressure it is given Under the influence of a pote° 

• From the Greek word meaning travder beesuw they travel from one point to another 
when a difference of potential is applied 



27 


Constituents 

Lial difference the ions move, those 
carrying a positive charge traveling in 
the direction of current flow, according 
to the convention described earlier, 
while negatively charged ions move 
in the opposite direction. If not ob- 
structed the ions would move wth a 
steadily increasing speed, acquiring in- 
creased energy, the maximum attained 
being dependent on the magnitude of 
the potential difference. Air normallj'^ 
contains a few ions, and if a potential 
is applied to two metal plates, or elec- 
trodes, in air, the ions are accelerated 
in one direction or the other according 
to their signs. 

2.16. In their motion through the 
gas, at least two things may happen: 
first, the ions may collide with gas 
molecules and be robbed of their en- 
ergi--, or second, suitable encounters 
may resvilt in the formation of more 
ions, a phenomenon known as ion- 
ization by collision. If the pressure of 
the air is in the region of atmospheric, 
the former effect will predominate, 
with the result that very few ions vn\\ 
be available for carrying the electric- 
ity. As the pressure is diminished, the 
latter effect becomes more important so 
that the number of ions produced by col- 
lisions gradually becomes larger than, 
and cventuallj’^ greatly exceeds, the 
number losing their energ}^ Hence the 
electric discharge passes mth increas- 
ing ease. At sufficiently low pressures 
the ionization decreases, because of the 
smaller number of collisions, and the 
discharge does not* occur so read- 
ily. 


of the Atom 

Cathode Bays 

2.17. By taking advantage of the 
fairly constant potentials that could 
be secured by means of the then re- 
cently invented voltaic battery, M. 
Faraday (1838) made the first sys- 
tematic studies of electric discharges 
through gases imder diminished pres- 
sure, Although he observed a number 
of interesting phenomena, he was lim- 
ited by the fact that the suction pumps 
available at the time for reducing the 
gas pressure were not too efficient. A 
great step forward was made, about 
1854, when H, Geissler, a German 
glass-blower of exceptional skill, not 
only developed an improved vacuum 
suction pump, but succeeded in sealing 
into glass tubes wires attached to metal 
electrodes. The evacuated Geissler 
tubes which he made were particularly 
suitable for the study of the passage 
of electricity through gases at low 
pressure, and with them J. Pliicker, 
in Germany, made numerous experi- 
ments between the years 1858 and 
1862. Among other things, he ob- 
served that the tube in the vicinity of 
the cathode, i.e., the electrode attached 
to the negative side of the source of 
potential,* emitted a green glow or 
luminescence.! The position of the 
glow could be changed by bringing a 
magnet up to the tube. 

2,18. The studies of electrical dis- 
charge through gases were continued 
in Germany by Pliicker’s pupil, W. 
Hittorf (1869), and by E. Goldstein 
(1876), From their observations they 
concluded that the luminescent glow 


electrode, i.c., the one joined to the positive side of the potential source, is 
caueci the anode. The words anode and cathode, derived from the Greek prefixes ana (ud) 
W Faraday (1834), at the suggestion of the O.xford philosopher 

^nmo manner ^ earlier, for the carriers of electricity, originated in the 

Phenomenon has often been described as "fluorescence” or "phosphorescence,” but 
lutnlrte not apply here (see §2.§2, footnotes). CoS 

lactoSolhcrK a Stempemto^ emissiomof light due to 



28 


Sourcebook on Atomic Energy Chap II 

on the tube was caused by “rays” Faraday cylinder, connected to an elec 
originating at the cathode, which Gold- trometer by means of which the sigr 
stem consequently called cathode rays and magnitude of electnc charge could 
The rays could be deflected by a mag- be determined It was found that i 
net and were able to cast a shadow of negative charge collected m the cjlm 
an obstacle placed in their path, diow- der, and so it u as argued that the raj^ 
mg that they traveled in straight lines v ere made up of negative particles 
219 Between the years 1879 and Objection v as taken to this conclusion 
1885 the English scientist William on the grounds that negatn ely charged 
Crookes, ^\ho designed improved vac- particles might ^/cll be ejected from 
uum discharge tubes, made a very the cathode, but there was no prooi 
comprehensive senes of investigations that they are identical with the cath 
of the electrical discharge From these ode rays 

he concluded that the cathode rays 2 21 The required proof was pro 
actually consisted of a stream of nega- vided m 1897 by J J Thomson the 
lively charged particles, which were famous English physicist, whose vork 
expelled from the cathode — the negv has had a profound effect, both direct 
live electrode — vith extremely high and indirect, on the study of atomic 
velocities This vicv of the nature of structure In the first place, he ro 
cathode rays supported a suggestion peated Pemn’s e penment and con 
made m 1872 by C F Varley, but it finned that charged particles are 
was opposed by many European physi- emitted bv the cathode But, in ad 
cists including such eminent men as dition, he sho\vcd that when the cath 
E Wiedemann (1880), H Hertz (1883) ode rays are deflected by a magnetic 
the discoverer of radio waves, and field, as indicated by the change in 
P Lenard (1894) The latter group position of the luminescence they pro* 
thought the cathode rays were an elec- duce, the negatively charged particles 
tromagnetic wave motion or vibration, arc correspondingly deflected Fur 
analogous to light waves but of shorter ther Thomson succeeded, where Gold 
wave length * If the rays arc really a stem and others had failed, in deflecting 
stream of charged particles then they the path of the cathode rays by means 
should be deflected by passage through of an electnc field Previous failures 
an electric field, as well as by a mag- had been due to excessu e ionization 
netic field, but Goldstein, m spite of of the gas still present in the discharge 

such effect However, the deflection of electnc field By working at very low 
cathode rays in the field of a magnet pressures Thomson minimized the in 
was an accepted fact, and this could fiuence of this ionization and then be 
not be explained if the rays were sim- was able to observe the anticipated 
liar to light waves deflection 

2 22 Now that it bad been estab- 

The Nature of Cathode Rays lished that the cathode rays are ac- 

2 20 In an apparently decisive ex- tually a stream of particles carrying 
penment, performed by J Femn m negative electncal charges, there still 
France in 1895, the cathode rays were remained the question of the identity 
allowed to fall on a device known as a of these particles As a result of nis 

• An explanation of the nature of light and related electromagnetic radiations is given » 
Chapter III 



29 


ConstituenUi of the Atom 


numerous experiments, Crookes had 
become convinced that the particles 
did not consist of ordinary matter; that 
is to say, they were neither solid, liquid 
nor gaseous. At the end of a lecture 
delivered before the Royal Society of 
London in 1879 he said: “The phe- 
nomena in these exhausted tubes re- 
veal to physical science a new world — 
a world where matter may exist in a 
fourth state.” In a confession of igno- 
rance, Crookes referred to this as 
the “ultragaseous” state. Subsequent 


events were to prove that there was, 
in fact, no such state of matter, but it 
was nevertheless true that the study 
of electrical discharges in gases at low 
pressures was bringing to light a “new 
world” of science. The elucidation of 
the real nature and significance of the 
negatively charged, cathode-ray par- 
ticles was the result of a number of 
converging studies; some of the more 
important of these will now be con- 
sidered. 


THE ELECTRON 


EiiUCTROLYSis: The Eahaday 

2.23. In the early years of the nine- 
teenth century, following the invention 
of the voltaic cell as a means of produc- 
ing an electric current, it was found that 
the passage of such current through 
aqueous solutions of acids, alkalies and 
salts was accompanied by chemical 
changes which were manifested by the 
appearance of specific products at the 
two electrodes. The process of decom- 
position, either of the water or of the 
substance dissolved in it, as the result 
of the passage of an electric current, 
was given the general name of elec- 
trolysis. For example, the electrolysis 
of a dilute solution of an acid, with 
platinum or other inert electrodes, al- 
most invariably results in the liber- 
ation of hj'drogen gas at the electrode 
(cathode) attached to the negative 
pole of the cell (or batterjO and of 
oxygen at the electrode (anode) joined 
to the positive pole. Sinrilarly, when 
an appropriate salt solution, for ex- 
ample, a solution of a zinc, copper, 
iron or mercurj* salt, is electrolyzed, 


the corresponding metal can be ob- 
served to separate at the cathode. 

2.24. Some of the most fundamental 
investigations in the field of electrolysis 
were made by M. Faraday (1831- 
1834), and as a result of this work he 
discovered that a given quantity of 
electricity always sets free at the elec- 
trodes chemically equivalent weights 
(§ 1.22) of different substances. In 
other words, it always requires the 
same quantity of electricity to liberate 
one equivalent weight of any sub- 
stance, irrespective of its nature. Care- 
ful experiments have shown that to set 
free exactly 1 gram equivalent, i.e., 
the equivalent weight in grams, of any 
substance at an electrode it is neces- 
sary to pass 96,500 coulombs* of elec- 
tricity; this quantity is called a fara- 
day. 


The AtoxucNatdbe or Euecttricity: 
The Elementary Charge 

2.26. In considering the significance 
of his results, Faraday wrote: “. . . if 
we adopt the atomic theory or phrase- 
• 'Hip coulomb is a convenient unit of quantitj* of electricity or electric chanre It corre- 



30 Sourcebook on 

ology, then the atoms of bodies which 
are equivalent to each other m their 
ordinary chemical action, have equal 
quantities of electncity naturally as- 
sociated ivith them ” In these words 
he implied the existence of a umt or 
atom of electncity, but apparently 
Faraday was not too sure of his ground 
for he was very cautious about com- 
mitting himself to this point of view 
Similarlv, the eminent English scholar 
J Clerk Maxwell, wnting m 1873 m 
his great Treatise on Electncity and 
Magnetism, thought that, in view of 
Faraday’s results, it might be con- 
vement to speak of a “molecular 
charge” of electncity But, be went on 
to say, “it IS extremely improbable 
that when we come to understand the 
true nature of electrolysis we shall 
retain the theory of molecular 
charges ” This was one of the few 
respects in which time proved Maxwell 
to be wrong 

2 26 It was left to the Irish physi- 
cist, G Johnstone Stoney who, dunng 
the years 1873 and 1874, wasamember 
of the Bntish Association Committee 
on the Selection and Nomenclature of 
Dynamical and Electrical Umts, to 
take the final plunge At the Belfast 
meeting of the Association in 1874, he 
read a paper On the Physical Units of 
Nature, which was not published until 

us m the phenomenon of electrolysis 
with a single definite quantity of elec- 
tricity which IS mdependent of the 
particular bodies acted upon For each 
chemical bond which is ruptured within 
an electrolyte, a certam quantity of 
electricity traverses the electrolyte, 
which IS the same in all cases If 
we make this our unit of electncity we 
shall probably have made a very un- 


Atomic Energy Chap U 

portant step m our study of moleculai 
phenomena ” 

2 27 On the basis of this argument 
the quantity of electncity, referred tc 
above as the faraday, which is asso- 
ciated With 1 gram equivalent of anj 
substance, should bear the same rela 
tionship to the postulated umt of elec 
tncity as the atomic weight does tc 
the weight of a smgle atom In othei 
words, the value of the umt quantity 
of electncity should be obtained upon 
dividmg the faraday by the Avogadrc 
number (§ 1 56) In 1868 Stoney, fol 
lowing Loschmidt, had made an esti 
mate of the latter number from kinetic 
theory equations, as already described 
and in his 1874 paper he used this 
result together with the best available 
datum for the faraday to denve a value 
of 3 X 10"“ electrostatic units (esu) 
for the unit of electncal charge • 

2 28 The concept of an "atomic 
unit of electncity received powerful 
support from the eminent German 
physicist H von Helmholtz In the 
Faraday Lecture of the Chemical So- 
ciety of London, m 1881, he said 
“Now the most startling result of Fara- 
day’s Law [that a given quantity of 
electncity always sets free chemically 
equivalent weights] is perhaps this 
if we accept the hypothesis that the 
elementary substances are composed 
^ .srAxd mwJudiiif 

that electncity also positive as well as 
negative, is divided into defimte ele- 
mentary portions which behave like 
atoms of electricity ” Similarly, at the 
Bntish Association meeting in 188o 
Oliver Lodge stated “This quantity 
the charge of one monad atom con 
slitutes the smallest known particle of 
electncity, and is a real natural unit 
2 29 By the early 1890s the ideaa 


• Using modem d&ta i e , 2 89 X esu for the faraday and 6 02 X 10• ** for the Avogadro 

number the umt is found to be 4 80 X 10^ e 8 u , as accepted at present 



31 


CoTistituents of the Atom 


expressed, above had beconie widely 
accepted, and Stoney, in 1891, pro- 
posed the name electron for the ele- 
mentary unit of electric charge. Thus, 
Faraday’s experiments on electrolysis, 
by logical development, led to the 
view that in solution every electrically 
charged atom, or perhaps group ^ of 
atoms, i.e., every ion, is associated with 
a definite whole number — one, two, 
three or more — of electronic charges. 
The number of unit charges associated 
vfith each ion is equal to its valence, 
i.e., the ionic (atomic or molecular) 
weight divided by its equivalent weight, j 

Gaseous Ions and the 
Eleiientary Chauge 

2.30. Since the foregoing conclusions 
were reached from studies of solutions, 
the estimated magnitude of the unit 
electronic charge, namely, about lO”'® 
e.s.u., could be regarded as applying 
only to the electrical carriers (ions) in 
solution. In the years 1890 to 1892, 
several attempts were made to deter- 
mine the unit charge associated vfith 
other electrically charged bodies, nota- 
bly by F. Richarz and H. Ebert, in 
Germany, and by A. Chattock, in 
England. Although some of the meth- 
ods used were based on theoretical 
considerations of doubtful validity, it 
is a remarkable fact that the values of 
the elementary or rmit charge were 
almost invariably found to be in the 
vicinity of 10"^® e.s.u., so that Chat- 
tock (1891) was moved to say: ‘T can- 
not help thinking that . . . [the re- 
sults obtained by a variety of methods] 
hyiiish strong grounds for supposing 
that electrified atoms in gases are asso- 
ciated with the same quantit}'- of elec- 
tricity as in electrolysis.” 

2.31. More definite confirmation of 
this point of view was obtained in 
England by J. S. Tomisend in 1897. 
If a solution of acid or alkali is elec- 


trolyzed with a large current, the gases 
—hydrogen and oxygen— which are 
liberated, are ionized. When these 
electrically charged gases are bubbled 
through water they form a dense cloud, 
apparently as a result of the conden- 
sation of moisture on the gaseous ions 
(§6.48). The cloud thus consists of 
minute drops of water carrying electric 
charges. From the total weight of the 
Avater contained in the cloud, and the 
average Aveight of a drop, derived from 
the measured radius and the knoAvn 
density, it is possible to calculate the 
number of individual drops in the 
cloud. ToAvnsend measured the total 
charge on the cloud by means of an 
electrometer, and knoAAung the niunber 
of drops present, it Avas a simple matter 
to determine the average charge asso- 
ciated with each drop. If the assump- 
tion is made that a gaseous ion upon 
which the moisture condenses carries 
a single elementary electric charge, 
this result is the magnitude of the unit 
(electronic) charge. The value found 
in this manner was 3 X 10“^®, later cor- 
rected to 5 X e.s.u., in satisfac- 
tory agreement Avith the unit charge 
born by ions in solution. Similar re- 
sults AA’ere obtained in the year 1898 by 
J. J. Thomson in his studies of the elec- 
tric charge carried by gaseous ions pro- 
duced by X-rays in their passage 
through air and hydrogen. (§ 2.83). 

Determination of the 
Electronic Charge 

2.32. By the turn of the century 
there was no longer any doubt about 
the existence of a definite unit of electric 
charge, namely, the electronic charge. 
Scientific interest then became cen- 
tered upon methods for the deter- 
mination of a really accurate value of 
this charge. In 1903, J. J. Thomson 
had used the rays emitted by radium 
(§ 2.105) to ionize the air, and had then 



32 


Sourc^ook on 

measured the average charge per ion, 
but this work did no more than supply 
further confirmation of views already 
established However, in the same 
year, a technical advance was made in 
Tliomson s laboratory in England by 
H A Wilson, later of the Rice Insti- | 
tute, Houston, Texas, and this proved 
to be the basis for some of the most 
important subsequent in\e3tigations 
He showed that it was possible to 
avoid the inaccurate and difficult de- 
termination of the total charge on 
the cloud of water droplets condensed 
upon ions, as used by previous workers, 
by studying the rate of fall of the cloud 
under gravity and also under the in- 
fluence of an electric field 

2 33 Further improvements were 
made in 1909 by F Ehrenhaft in 
Austna and by R A Millikan m the 
United States, instead of making ob- 
servations on a cloud as a whole, and 
BO obtaining a gross average, Chren- 
haft studied individual suspended par- 
ticles of gold, silver, platinum and 
phosphorus, while Millikan worked 
'with single water droplets Later 
(1911) Millikan used oil, instead of 
water, to form the droplets, and thus 
eliminated errors due to evaporation, 
and consequent change in wei^t of the 
drops, during the course of an expen- 
ment 

2 34 In outline, Millikan’s appa- 
ratus consisted of two horizontal metal 
plates about 22 cm diameter and 1 6 
cm apart, as indicated by A and B m 



Fio 2 1 Diagrammatic representation of 
apparatus used by Millikan to determine 
electromc chaige 


Atomic Energy Chap U 

Fig 2 1 The plates were supported m 
a closed vessel contammg air at low 
pressure, and were connected to the 
poles of a high-voltage (10,000 volts) 
battery, V In the upper plate there 
were a number of small holes, as mdi 
cated at C By means of an atomizer 
a fine spray of a nonvolatile oil was 
introduced into the vessel, as a result 
of friction m the atomizer, the droplets 
of oil so obtained were electncally 
charged From time to time, one of 
these droplets would pass through the 
hole C, and then it could be observed 
by means of a telescope (not shown in 
figure) By using the illumination of a 
powerful beam of light, entering the 
window W (at left), the droplet ap- 
peared as a bnght star on a dark back 
ground 

2 36 With the battery V discon 
nected, the droplet fell slowly under 
the influence of gravity, and the rate of 
fall was measured "This rate, or ve- 
locity, represented by vi, is dependent 
on the mass m of the droplet, and a 
given by the equation 

Vi ( 21 ) 

where g is the gravitational constant 
(981 cm per sec per sec ), and is a 
proportionality constant which is re- 
late to the viscosity of the air and 
the size of the oil droplet The high 
voltage battery was then switched on 
thus produemg an electric field, the 
direction bemg such as to make the 
charged droplet move upward, against 
the force of gravity If is the 
strength of the electric field, i e , the 
voltage of the battery divided by 
the distance between the plates, then 
the upward force actmg on the droplet 
18 Ee„, where Cn is the charge earned by 
the droplet Smee this is opposed by 
the gravitational force mg, the net 
ward force is Ecn ~ mg, the upward 



33 

( 2 . 6 ) 


Constituents of the Atom 


velocity of the oil droplet, ■which is 
measured, is then represented by 


vz = h{Ee„ - mg), (2.2) 

the proportionality constant h having 
the same significance as in equation 
(2.1). If one of these two equations is 
divided by the other, the constant k 
cancels out, and the result is 

h = — M (2.3) 

Vz Ecn - nig 

or 

Cn = ^ (Vl + Vz). (2.4) 


2.36. Since the quantities. Di, vz, E 
and g are available, it should be pos- 
sible to calculate the charge e„ carried 
by the oil drop, provided its mass m 
were kno^^^l. In order to determine 
the latter, Millikan, like several of his 
predecessors, employed an equation, 
derived by the English mathematician 
G. G. Stokes, applicable to small spher- 
ical drops falling undey the influence of 
gravity. According to Stokes, the ve- 
locity vi, v-ith which the droplet falls in 
air under the influence of gravity alone, 
is related to the coefficient of "viscosity, 
i.e., resistance to flow, t? (Greek, eta), 
of the air and the radius r of the drop 
hy 


2g}^d 

Vi = -r — > 

9jj 


(2.5) 


where d is the density of the oil of 
which the drops are made. Since Vi 
has been determined, as described 
above, and g, ij and d may be regarded 
as known, the radius r of the drop can 
he obtained from equation (2.5). 

2.37. If the oil drop is spherical, as 
Jwsumed, the mass m is related to the 
radius r by 


m = 47rr®d/3, 

the quantity tt having its usual signifi- 
cance. The value of r has just been 
derived, and the density d of the oil is 
known; hence the mass m of the drop 
can be calculated. Upon inserting this 
result into equation (2.4), together 
with the measured velocities vi and vz, 
the magnitude of the charge e„ carried 
by the oil droplet can now be deter- 
mined. 

2.38. By exposing the air in the 
vessel in Fig. 2.1 to the action of 
X-rays, Millikan caused gaseous ions 
to form, and occasionally an oil drop 
would attach itself to one of these ions 
with a consequent change in the value 
of c„, the charge of the droplet. The 
new upward velocity Vz of the oil drop 
in the electric field was measured, and 
On recalculated, vl and m remaining 
unchanged. Sometimes the droplet ac- 
quired a positive charge and sometimes 
a negative charge, but the experi- 
mental method wms the same, except 
that the high-voitage battery connec- 
tion had to be reversed. 

2.39. As a result of a large number 
of measurements, Millikan found that 
the charge Cn was always an integral, 
i.e., a -whole number, multiple of a 
definite elementary charge, which -urns 
presumably the electronic charge. After 
applying numerous corrections to the 
foregoing equations, Millikan con- 
cluded, in 1917, that the most reliable 
value of the unit charge wms 4.774 X 
10~“ e.s.u. For several years, this 
value was widely accepted, but in 1928 
the work of E. Backlin, in Sweden, and 
of J. A. Bearden, in the United States, 
began to throw some doubt upon its 
accurac3\ 

2.40. By the middle of the second 
decade of the present centurj’’, the 
faradaj'^ (§ 2.24) had been determined 
with great care both in the United 



34 


Sourcebook on Atomic Energy 


States and m England, and hence its 
value was known with some certainty 
An accurate determination of the Avo- 
gadro number would then have per- 
mitted the evaluation of the electronic 
charge, utilizing the principle first em- 
ployed by Stouey (§ 2 27) If the wave 
lengths of X-rays were available, then 
the Avogadro number, and conse- 
quently the electronic charge, could 
be obtained from diffraction studies 
m crystals (§ 2 87) In 1926, A H 
Compton and R L Doan, in the 
Umted States, rfiowed how X ray 
wave lengths could be measured by 
means of a ruled line gratmg (§ 3 10), 
and it was as a result of experiments of 
this kind that Backlin and Bearden 
found the electronic charge to be 
slightly higher than Millikan’s value, 
namely, 4 80 X 10““ e s u Other in- 
vestigators, using a generally similar 
procedure, subsequently confirmed this 
result 

2 41 Although the difference be- 
tween 4 77 X 10-« and 4 80 X 10“« 
may not appear large, it is much 
greater than the known experimental 
errors m the respective methods Many 
scientists were concerned with this dis 
crepancy, and m 1932 E Shiba, of 
Japan, suggested that the value for the 
viscosity of the air used by Millikan 
m equation (2 5), might have been m 
error Actually, MiUikan had adopted 
what he thought was the most reliable 
pubhshed datum, but, as events turned 
out, this proved to be incorrect Upon i 
recalculatmg the results of his expen- 
ments, making use of more recent vis- I 
cosity determinations, Milhkan found | 
the elementary electronic charge to be 
m good agreement with that given by I 
the X-ray method At the present , 


Chap II 

time, from various studies^ using both 
oil drop and X-ray diffraction pro- 
cedures, the unit electronic charge is 
confidently known to be very close to 
4 802 X 10~“ e s u * T!Tiis value ap- 
plies to both positive and negative unit 
charges 

Specitio Crahoe of Cathode 
Ray Particles 

2 42 It IS opportune, at this point, 
to revert to a consideration of the 
cathode rays which, m 1897, J J 
Thomson showed to consist of a stream 
of negatively charged particles origi- 
nating from, or in the vicmity of the 
negative electrode, i e , the cathode, of 
an evacuated discharge tube (§ 2 21) 
Even before this tune, while the con- 
troversy as to the nature of the cathode 
rays was still m progress, experiments 
and calculations bad been made on the 
properties of the rays, in the event that 
they should prove to consist of charged 
particles If a stream of such particles 
moves initially m a straight line, and a 


0 0 O 0 o o 

M»SM£fCfeL0 H 
0 9 0 0 0 0 



Fro 2 2 Path of charged particle moving 
in a magnetic field at right angles to direc- 
tion of motion 

magnetic field is appbed m a direction 
at right angles to the direction of mo- 
tion the particles will be forced by the 
field to follow a circular path (Fig 2 2) 
If e IS the magnitude of the charge 


• In the period 1914 to 1916 a controversy raged between F Ehrenhaft on the one hand 
andll A Millikan, on the other hand as to the d^entary nature of the electron The former 
contended that he had proved the existence of a sub-electron, having a charge smaller than 
the accepted value The latter, however, refused to accept the evidence and there is little 
doubt tlwt hiB stand was justified 



35 


Constituents of the Atom 


carried by each particle and v is the 
velocity with which it moves, the mag- 
netic force acting on a particle is JJeOf 
where H is the magnetic field strength. 
This force is exactly balanced by the 
centrifugal force mv^/r of the particle 
of mass m, moving under the influence 
of the field, in a circular path of radius 
r. , Hence, equating the two expres- 
sions, 


so that 


The strength H of the magnetic field 
may be regarded as known, and so if 
the velocity of the charged particles 
and the radius of curvature of the cir- 
cular path tliey follow could be meas- 
ured, the value of e/m, i.e., the ratio of 
their charge to mass, sometimes called 
the specific charge, could be determined 
by means of equation (2.8). 

2.43. The foregoing considerations 
apply to any charged particles irrespec- 
tive of charge and mass, and they w^ere 
applied by A. Schuster in England, in 
1890, to cathode rays. He measured 
the radius of the circular path in a 
magnetic field vdthout difl&culty, but 
his estimate of the velocity of the par- 
ticles was highly approximate. a 
res\ilt his value of e/m Avas incorrect, 
and he drew the erroneous conclusion 
that the cathode-ray particles were 
negatively charged, gaseous atoms, 
probably nitrogen ions. In the early 
part of 1897, both E. Wiechert and W. 
Kaxifmann, in Germany, reported re- 


Hev = 


inv^ 


£ 

m Hr 


(2.7) 

( 2 . 8 ) 


suits of measurements on the path of 
cathode rays in a magnetic field.' Their 
determinations of the velocity of the 
particles — about one-tenth of the speed 
of light, i.e., 3 X 10® cin. per sec.-- 
proved to be fairly accurate and their 
values of e/m, expressing the charge 
e in e.s.u. and the mass m in gramsj 
were approximately 10^'^ e.s.u. per 
gram.* Kaufmann found the value of 
e/m for the cathode-ray particles was 
the same irrespective of the nature of 
the gas present in the discharge tube, 
or of the conditions of the discharge. 
By comparing his results with the e/m 
calculated for a hydrogen ion in so-- 
lution, approximately 3 X 10^^ e.s.u. 
per gram,t Wiechert concluded that 
the particles had a mass of something 
between a one-thousandth and a four- 
thousandth part of the mass of a hy- 
drogen atom (or ion). However, it was 
left to J, J. Thomson to appreciate the 
importance of similar results, which he 
obtained independently, and to inter- 
pret their significance. 

Thomson’s ExPEKiirENTS 

2.44. Because of the part they played 
in the study of atomic structure, 
Thomson’s experiments, although not 
of the greatest accuracy, have become 
classical. In order to determine, the 
velocity of the cathode-ray particles, 
required in connection with equation 
(2.8), he made use of an idea which, 
curiously enough, had been indicated 
in 1883 by H. Hertz, one of the oppo- 
nents of the view that the cathode rays 
consist of charged particles. A moving 
charged particle can be deflected from 
its initial path by the application of 


to generally mvolve studies in a magnetic field, it is the custom 

SrCr mo/ W rather than in electrostatic units. 

* avoid the confusion resulting from the employment of different 
'1 ^ converted into e.s.u. upon multiplying by a factor of 3 X 10«. 
ion bfolS the umt (electronic) charge earned by a hydrogen 

gmm (I l.M) ’ ^ ^ hydrogen atom (or ion) 1,6 X 



36 


Sourcebook on Atornie Energy 


CJther an electric or a magnetic field 
As seen m § 2 35, the force acting on a 
particle of charge e in an electric field 
of strength E is Ee, whereas m a mag- 
netic field of strength H, the force, as 
stated above, is Hev, where ti is the 
speed of the particle If the electric 
and magnetic fields are arranged so 
that their effects on a moving charged 
particle exactly compensate each other, 
and the particle is not deflected from 
its path, it follows that 

Ilev = Ee, (2 9) 



It should thus be possible to determine 
the speed of motion v of electrically 
charged particles from the strengths of 


Cha'p II 

rays were subjected to the action of an 
electric field, and a magnetic field was 
applied by means of a magnet M out- 
side the tube The deflection of the 
beam was studied by observing the 
luminous spot produced by the ra>s 
when striking the wall of the tube at 
the extreme right, a scale F permitting 
actual measurement After noting the 
position of the undeflected beam, i e , 
with neither electric nor magnetic 
fields operating the magnetic field H 
only was applied, and from the de- 
flection the radius of curvature r of the 
circular path could be calculated 
Then the electric field was put on and 
Its magnitude E was adjusted so as to 
bring the luminous spot back to its 
original position Thus the informa- 
tion required to determine v by equa- 
tion (2 10), and hence e/m by equation 
(2 8), was available 



Fig 2 3 Thomson s method for studying charged particles by deflection 
in electnc and magnetic fields 


the compensating electnc and mag- 
netic fields Introduction of this re- 
sult into equation (2 8) ivill permit e/m 
to be obtained from the radius of 
curvature of the path in the mimetic 
field alone 

2 46 The experimental procedure 
used by Thomson may be explained 
by means of Fig 2 3 The rays were 
emitted from the cathode C, m an 
evacuated tube, passed through a hole 
in the anode A, and a narrow beam 
was picked out by the sht S By con- 
necting the plates PP, wnthm the tube, 
to a source of high voltage, the cathode 


2 46 In agreement with previous 
workers, Thomson found that the 
cathode-ray particles moved ivith the 
enormous speed of 3 X 30® cm per 
sec , and that c/m was about 2 X 10*^ 
e s u per gram Further, he noted that 
the results were the same for different 
cathode materials, namely, aluminum, 
iron and platmum, and also for differ- 
ent gases, air, hydrogen and carbon 
dioxide, present m the discharge tube 
Hence, Thomson concluded that the 
“earners of the electric charge m the 
cathode rays are the same whate\er 
the gas through which the discharge 


37 


Constitiients of the Atom 


passes.” He went on to say: “The 
explanation which seems to me to ac- 
count in the most simple and straight- 
forward maimer for the facts is founded 
on the view of the constitution of the 
chemical elements which has been fa- 
vorably entertained by many chemists: 
this \uew is that the atoms of the dif- 
ferent chemical elements are differ- 
ent aggregations of . . . [ultimate par- 
ticles] of the same kind. ... If, in the 
very intense field in the neighbourhood 
of the cathode, the molecules of the gas 
are . . . split up, not into ordinary 
chemical atoms, but into these pri- 
mordial atoms which we shall for 
brevity call corpuscles; and if these 
corpuscles are charged vdth electricity 
and projected from the cathode bj'- the 
electric field, they would behave ex- 
actly like the cathode rays. This would 
evidently give a value of in/e [or e/m] 
which is independent of the nature of 
the gas ... for the carriers are the 
same whatever the gas may be. . . . 
Thus we have in the cathode rays 
matter in a new state, a state in which 
the subdivision of matter is earned 
very much further than in the ordinary 
gaseous state; a state in which all 
matter — ^that is, matter derived from 
different sources such as hydrogen, 
oxygen and carbon — is one and the 
same kind; this matter being the sub- 
stance from which all the chemical 
elements are built up.” Thus, the 
negatively charged, cathode-ray cor- 
puscles were believed by Thomson to 
be the ultimate particles of which all 
matter was constituted. 

2.47. As seen above, the e/m value 
found for the corpuscles was roughly 
a thousand times greater than for the 
hydrogen ion in solution; for this differ- 
ence there were two possible expla- 
nations. Either the charges e were 
approximately the same, so that the 
cathode-ray particles would be some- 


thing like a thousand times lighter 
than a hydrogen atom, or the masses 
m might be of the same order, in which 
case the corpuscles would carry a much 
larger charge than the elementary elec- 
tronic charge. As indicated earlier 
(§ 2.43), Wiechert apparently favored 
the former view. Thomson, on the 
other hand, was at first inclined to the 
latter alternative, but further experi- 
mental work caused him to change his 
mind. 

The Electeon as a Paeticle 

2.48. In 1899, Thomson set out to 
resolve the doubt concerning the sig- 
nificance of the e/m values of the cor- 
puscles by determining directly their 
charge, as well as the charge-to-mass 
ratio. Unfortunately, this could not be 
done with the cathode-ray particles, 
and so he turned to another source. 
It was well knoum toward the end of 
the nineteenth century that ultraviolet 
light falling on certain metals, par- 
ticularly zinc, was associated with the 
emission of negatively charged par- 
ticles, a phenomenon known as the 
photoelectric effect. Thomson deter- 
mined the e/m ratio for these particles, 
by means of electric and magnetic 
fields, and found it to be virtually the 
same as for the cathode-ray corpuscles. 
Charged particles produced bj'^ an in- 
candescent filament, i.e., by the therm- 
ionic effect, also had a similar e/m 
value. Utilizing the cloud method, de- 
scribed in § 2.31, Thomson measured 
the charge on the photoelectric par- 
ticles; this turned out to be not essen- 
tially different from the unit electronic 
charge. In \aew of the constancy of 
e/m for the negatively charged par- 

I tides produced in different ways, it was 
reasonable to conclude that the parti- 
cles were identical. 

2.49. In the words of Thomson: 
“The experiments just described, taken 



38 


Sourcebook on Aiotnic Energy Chap II 

m conjunction with previous ones 2 62 As matter is normally elec- 

on cathode rays, show that in gases at tncally neutral, that is to say, it is not 
low pressures negative electrification, electrically charged, it follows that 
though it may be produced by very differ- there must be something in the atom 
ent means* is made up of units each which cames a positive charge to bal 
having a charge of electricity of a ance the negative charge of the elec- 
definite size, the magnitude of this irons This matter ivill be considered 
negative charge is equal to the more fully in Chapter IV In the 
positive charge earned by the hydro- meantime, it may be stated that the 
gen atom [ion] m the electrolysis of positive charge is an integral part of 
solutions ” the atom, but the electrons can be 

2 60 Smee their charge is equal to made to pass from one atom to an- 
that earned by a hydrogen ion, it is other A negatively charged body is 
clear that the mass of the negative thus one which contains more electrons 
particles, irrespective of their origin, than in the normal, or neutral, state, 
must be about a thousandth part of a positively charged body is one with 
that of a hydrogen atom As Thomson fewer electrons than m the neutral 
pointed out, these are the lightest par- state Thus, when glass is rubbed mth 
tides hitherto recognized as capable of silk, electrons pass from the glass to the 
a separate existence The fact that the sitk so that the former acquires a posi- 
same partides are produced m different tive electric charge and the latter a 
ways — by electric discharge and by negative charge A positive ion is an 
photoelectnc and thermionic effects — atom or group of atoms which has been 
lends support to the view that they arc depnved of one or more of its electrons, 
ultimate constituents of all matter whereas a negative ion is an atom or 
2 51 Because the charge on the par- group which has acquired additional 
tides present in the cathode rays, and electrons 

associated with the thenuiomc and 2 63 A flow of electric current is 
photoelectnc effects, was identical with invanably accompamed by a flow of 
the elementary electromc charge, the electrons from one pole to another 
name electron, onginally intended by Since the electron cames a negatue 
Stoney (§ 2 29) for the magnitude of charge the direction of flow is opposite 
the charge, soon became associated that of the conventional flow of the 
with the actual partides themselves positive electnc current This sppar- 
Possibly m the interest of stnet ac- ently anomalous situation is the re- 
curacy, Ihomson adhered to the term suit of Franklin's someuhat arbitrary 
corpuscle for about twenty years, but choice of electnfied glass as positive 
ultimately he gave it up m favor of rather than negative (§ 2 4) If he had 
electron At the present time, the made the opposite choice, the con- 
electncally charged particles, carrying ventional charge of the electron would 
aTicgahvechargeof 4 802 X 10"“e s u , have been described as positive, in- 
and having a mass slightly more than stead of negative The direction of 
a two-thousandth part of that of a flow of the positive current would then 
hydrogen atom, are called electrons have been the same as that of the 
They are undoubtedly fundamental electrons 
constituents of all material atoms 

• The present writer has italicized this phrase because of its importance 



39 


Constituents of the Atom 


Specific Charge of the j 
Electron 

2.64. During the present century 
numerous determinations of the spe- 
cific charge, i.e., of the charge-to-mass 
ratio, of electrons have been made. 
Some of these depend on a study of 
their behavior in various types of elec- 
tric and magnetic fields, while others 
are based on spectroscopic measure- 
ments. It will be explained later 
(§4.42) how the characteristic light 
emitted, or absorbed, by an atom, 
known as its spectrum, is determined 
by the electrons. Consequently, rela- 
tionships have been developed among 
the properties of the electron and the 
frequencies, or wave lengths, of spec- 
tral lines. 

2.66. Further, as the Dutch physi- 
cist P. Zeeman showed in 1896, certain 
of these spectral lines are split up into 
component lines when the substance 
emitting the spectrum is placed in a 
very intense magnetic field. The fre- 
quency difference between the com- 
ponents is related to the field strength 
and also to the specific charge e/w of 
the electron. From his earliest meas- 
urements of the splitting of spectral 
lines in a magnetic field, Zeeman cal- 
culated the specific charge of the elec- 
tron to be about 3 X 10^^ e.s.u. per 
gram, in striking agreement with the 
value obtained in the same year by 
Thomson, and others, from cathode- 
ray studies. The frequencies of spectral 
lines can now be measured with great 
precision, so that e/m can be obtained 
with a high order of accuracy. The 
general conclusion, from experiments 
of various kinds is that the best value 
for the specific charge of an electron is 
5.273 X 10’’ e.s.u. per gram. 


Mass and Size of the Electron 

2.66. Since both the actual charge e 
and the specific charge e/m of the elec- 
tron are now known, it is obviously a 
simple matter to calculate the mass m 
of a single electron. All that is neces- 
sary is to divide e, which is 4.802 X 
10“’® e.s.u., by e/m, i.e., 5.273 X 10” 
e.s.u. per gram, and the result is 9. 106 X 
10-28 gram for the mass of an electron. 
Upon comparing this with the mass of 
a hydrogen atom, i.e., 1.673 X 10“=* 
gram, it is seen that it would require 
1838 electrons to have the same mass 
as an atom of hydrogen. On the usual 
chemical atomic weight scale, with 
atmospheric oxygen being assigned a 
value of 16.000, the weight of an elec- 
tron is 0.000548, as is found either 
upon multiplying the actual electron 
mass by the Avogadro number or by 
dividing the atomic weight of hydrogen 
by 1838. The electron is thus con- 
siderably lighter than the atom of even 
the lightest element. 

2.67. Attention should be called 
here to the fact, W'hich will be under- 
stood later (see Chapter III), that the 
apparent mass of an electron depends 
on the speed with which it is moving. 
The mass value recorded here is appli- 
cable -when the electron is either at rest 
or moving at a relatively low speed, 
say, less than about one tenth of the 
velocity of light.* It is consequently 
referred to as the rest mass of the 
electron. 

2.68. After the discovery of the elec- 
tron and the realization of its ex- 
tremely small mass, the possibility was 
considered that this might be due en- 
tirely to its electric charge. In the 
scientific sense, a body is said to have 
mass or inertia wiien energy (work) 


velocity of light is close to 3 X 10"> cm. per see. (§3.14), so that one tenth of the 

'wwrbul i'^liiVv ^ r actually a very high 

• ivettl, but u nia\ be regarded as relatively slow compared with the speed of light. ^ 



40 


Sourcdtook on Atomic Energy Chap 11 

must be supplied to set it m motion mg relatively slowly, and hence the 
In other words, if energy is required to rest mass of the electron may be used 
start a body movmg, it must, by the Taking e as 4 80 X 10-*V3 X 10*® 
definition, possess mass, in its most emu and m as 9 1 X 10“^ gram, the 
general sense Amoving electric char^, radius of the electron is found from 
no matter what its nature, produces a equation (2 11) to be 2 X 10”'* cm 
magnetic field in its vicinity, and since This figure may be taken as an indi- 
theestablishmentofsuchafieldrequires cation of the size of an electron, on the 
energy, it follows that energy is needed basis of two assumptions first, that its 
to set the charge in motion Conse- charge is uniformly distnbuted over a 
quently, the charge must be associated spherical surface, and second, that its 
with mass or, at least, with something rest mass is purely electromagnetic in 
that behaves like, and therefore can- nature, that is to say, assuming the 
not be distinguished from, mass Such apparent mass of the electron to be 
mass IS said to be electromagnetic due entirely to its charge * If it should 
Since the electron cames an electric transpire that part of the mass is due to 
charge, and does, in fact, produce a other causes, the radius u ould be even 
magnetic field when in motion, it must smaller than 2 X 10~** cm The result 
have, at least, electromagnetic mass cannot be regarded as \ery exact, in 
If the assumption, is now made that any event, because it is doubtful 
the mass of the electron derived above whether the theory used in the denva- 
js entirely electromagnetic, it is pos- tion of equation (2 11) is applicable to 
Bible to calculate the radius of an a particle as small as an electron How- 
clectron ever, m so far as a radius can be attnb- 

2 B9. Several years before he had uted to an electron (see § 3 44), it is 
become interested m cathode rays, probably safe to say it is about 10"'* 
J J Thomson in 1881 had derived an cm 

equation, from theoretical principles, 2 60. As mdicated in § 1 65, the 
relating the electromagnetic mass m of radii of most atoms are m the vicinity 
a spherical charged particle of radius of 2 X 10"® cm , and consequently the 
r, to Its charge e expressed m electro^ radius of the electron is about 10”®, i e , 
magnetic units (see §2 43, footnote), one hundred-tfiousandth, of the radius 
thus, of an average atom In the bowl of 

2e^ (2111 magmfied to the size of the 

^ ~ 3771 earth, referred to in § 1 55, an electron 

would be so small that it would be 
This equation is strictly applicable bardy visible in a good optical micro- 
only when the charged particle is mov- scopel 

POSITIVELY CHARGED PARTICLES 

Positive Rais and the Proton that search should be made for a corre- 
2 61. After the discovery of the neg- spending particle carrying a positive 
atively charged electron, it was natural charge In 1886, E Goldstein, m Ger- 

* Although J J Thomson was responsible for the definite proof of the existence of the 
electron, and also for the derivation of the equation for electromagnetic mass I/ord Rayleigh, 
in The Life of Str J J Thomson, Cambndge University Press, 1942, says that he did not at 
first favor the idea that the mass of the electron was entirely electromagnetic in origin, but it 
became accepted because of its advocacy by Obver Lodge and others 



41 


Constituents of the Atom 


many, had used a perforated metal disc 
as a cathode in a discharge tube, and 
observed luminous rays emerging in 
straight lines from the holes on the side 
opposite the anode (Fig. 2.4), These 
rays were originally called canal rays, 
since they passed through holes, or 
channels, in the cathode.* By collect- 
ing the rays in a Faraday cylinder, 
J. Perrin (1895) showed that they were 
associated with a positive charge, and 
this was confirmed by W. Wien in 1898 
by studying their deflection in electric 


*€ 


SNOOC 




POSITIVE RATS 




PERFORATED CATHODE 




Fio. 2 . 4 . Positive rays emerging from 
holes in the cathode on the side away 
from tile anode. 


and magnetic fields. Consequently, 
J. J. Thomson later (1907) proposed 
the more appropriate name positive 
rays, and this has been universally 
adopted. 

2.62. In the course of his work, Wien 
had determined the charge-to-inass 
ratio (e/772) of the particles present in 
the positive rays, and found that the 
values were very much smaller than 
that for electrons, and often less than 
for the hydrogen ion in solution. As- 
suming, as is very probable, that the 
charge carried by the positive particles 
is a small integral number of elemen- 
tarjF charges, the only conclusion to be 
drawn is that the particles in the posi- 
tive rays are much heavier than elec- 
trons, being actual atoms or molecules 
which have become electricall}’’ charged . 
With a discharge tube containing air, 
W icn found the masses of the particles 
indicated that they consisted of oxj'- 


gen or nitrogen molecules. Subsequent 
work proved that, in general, the 
masses of the positively charged par- 
ticles were determined by the gas 
present in the discharge tube. 

2.63. Apart from the sign of the 
electric charge, the positive rays thus 
differ in twm respects, at least, from 
cathode rays. In the first place, the 
particles in the positive rays consist of 
actual atoms or molecules, whereas in 
the cathode rays they are very much 
smaller and lighter even than hydro- 
gen; and, in the second place, the cath- 
ode ray particles are independent of 
the nature of the gas in the discharge 
tube or of the cathode material, but in 
the case of the positive rays the par- 
ticles are usually charged atoms or 
molecules related to the gas in the 
tube. 

2.64. In spite of a very thorough 
search, no positively charged particle 
similar to the electron was found in the 
discharge tube. The lightest particle 
so observed, which the New Zealand- 
born physicist Ernest Rutherford, in 
1914, described as the “long sought 
positive electron,” had the same mass 
as the hydrogen atom and carried one 
unit (positive) charge, equal in mag- 
nitude, but of opposite sign, to the 
charge carried by an electron. In 
other words, it is a singly charged, posi- 
tive hydrogen ion, H+. This presum- 
abljF consists of a hydrogen atom from 
which one electron has been removed, 
apparently as a result of a collision in 
the discharge tube, leaving it vdth an 
equivalent positive charge.f By 1920, 
a number of circumstances, to which 
reference will be made in Chapter 
Vin, had arisen, indicating that the 
positively charged hydrogen atom just 
described represented an important 


"cwtni" translated as 

relmcd to te | in accord with the ideas c-xpressed bj' Benjamin Franklin 



42 


Sourcehooh on Atornie Energy 


unit m the structure of other atoms 
The name proton was consequently as- 
cribed to it * Since the weight of the 
hydrogen atom is 1838 times that of 
the electron, it follows that the weight 
of a proton, which is a hydrogen atom 
minus one electron, is 1837 times aa 
great as that of an electron 

The Positive Electron 
OR Positron 

2 66. In spite of the absence of ex- 
perimental evidence for the existence 
of a positive electron, i e , a particle 
similar m mass to the electron but 
carrying a positive charge, the English 
mathematical physicist PAM Dirac 
had, in 1930, presented some theoreti- 
cal arguments indicating that such a 
particle was possible Dirac’s discus- 
sion was of a highly abstruse character, 
but it may be summarized, somewhat 
superficially, as follows Ordmary neg- 
atively charged electrons must be able 
to exist in two different types of energy 
states, called positive and negative 
These terms have no relationship to 
the electric charge, but refer to energy 
values relative to a certain, zero state 
If one of the possible negative energy 
states IS not occupied by an electron, 
there is a vacancy — sometimes referred 
to as a Dirac ’‘hole,” although it is not 
a hole in the ordmary three-dimen- 


Chap II 

sional sense — which should behave like 
apositively charged electron inth posi- 
tive energy 

2 66. At first Dirac thought that 
this represented a proton, since no 
positive electron had been observed, 
but it was soon seen that such could 
not be the case In the first place, the 
mass of the proton is much greater 
than that of the electron, whereas the 
theory required the positive particle 
to have the same mass as the negative 
electron In the second place, since 
Dirac’s hypothetical positive electron 
is really a vacant “hole,” it can readily 
be filled by an ordinary negative elec- 
tron In other words, the positive 
electron should have a very short hfe, 
because a negative electron, of which 
there are many always available, should 
quickly combine with it The two 
charges will then neutralize and annihi- 
late one another, leaving nothing but 
energy (§ 3 80) Actually, the proton 
is quite stable, and so it cannot satisfy 
the requirements of the particle which 
would be the equivalent of the Dirao 
“hole ” 

2 67. Proof of the existence of the 
long-sought positive electron was fi- 
nally obtained by C D Anderson, at 
the California Institute of Technology, 
m 1932 In order to study the so-called 
cosmic rays (see Chapter XVII), which 


• From the Greek protoa (first) Various reports concerning the ongm of the term proton 
are to be found m the scientific literature The following is a quotation from a footnote by 
E Rutherford to a paper by O Masson xmtten in 1920 'The question of a suitable name 
for this unit p e , the positively charged hydrogen atom] was discussed at an informal meeting 
of a number of members of Section A [Physics] of the British Association at Cardiff this year 
The name ‘proton’ met with general approval, particularly as it suggests the term 
‘protyle’ given bv Prout in his well known hypolhwis [§ 1 38] that all atoms are built up of 
hydrogen The ne^ of a special name for the unit of mass 1 was drawn atten 
tion to at the Sectional Meetmg, and the wnter [Rutherford] then suggested the name 
‘proton ' ” It should be noted that Rutherford does not claim to have made the ongiruu 
suggestion, but only to have put it forward at the formal meeting of Section A Lodge refer- 
ring to the matter says “At the Cardiff Meeting of the British Association Sir Ernest 
Rutherford suggested or tentatively approved the suggoetion, that the name ‘proton’ should 
be applied to tlus hydrogen unit of positive charge '* There is thus some doubt concern 
ing the identity of the individual who su^ested the name m this particular connection 
Actually, the term proton is to be found m the scientifio literature as far back as 190S and 
possibly earlier, being used in a general sense to refer to the fundamental unit, analogous to 
protyle, from which all elements are built up 



43 


Constituents of the Atom 


appear to come from outer space, 
Anderson, in conjunction with R. A. 
Millikan (§ 2.33), had constructed an 
apparatus, known as a cloud chamber 
(I 6.50), which was placed in a very- 
strong magnetic field. In the cloud 
chamber the path of an electrically- 
charged particle can be rendered vis- 
ible, and actually photographed. The 
intensity of the track pro-vides infor- 
mation concerning the mass of the 
particle, and the direction in which it 


depending on the amount of energy 
lost in the plate. Measurements made 
on the track of a particle before and 
after it has passed through a plate, 
together -with observations of the den- 
sity of the track itself, give definite in- 
formation about the mass of the par- 
ticle and the magnitude of the electric 
charge it carries.” 

2.69. One of the numerous photo- 
graphs obtained in this manner, with, 
the lead plate seen cutting across the 



Fig. 2.5, Cosmic-ray photograph obtained 
by Anderson which led to the discovery of the 
positron. 


is bent in the magnetic field indicates 
whether the charge is positive or neg- 
ative. 

2.68. Wlien the cloud chamber was 
operated, numerous tracks were ob- 
served due to charged particles result- 
ing from the impact on matter of the 
very highly energetic cosmic rays. A 
lead plate of 6 mm. tliickness was 
placed across the chamber with the 
object of depriving the particles of 
.some of their cnerg 3 ', and, as Anderson 
stated in his Sigma Xi Lectures in 
1939, “the degree of the cunmture in 
the magnetic field shows a difference. 


center, is shovTi in Fig. 2.5; it is a 
photograph of historical significance, 
for its interpretation by Anderson led 
to the discovery of the positive elec- 
tron. Since the curvature of the track 
is less below the plate than above, the 
energy of the particle is greater below 
the plate. Hence the particle must have 
been moving upward. Knondng the 
direction of the magnetic field, and 
the direction of motion of the particle, 
the curvature of the track to the left 
immediately slioAved that the particle 
must be positively charged. The den- 
sity of the track -w^as less than would be 



46 Sourcebook on 

a positron does not exist for any ap- 
preciable time The average life of a 
positron varies with its environment, 
but it 13 usually of the order of a 
billionth part (10~*) of a second In j 
view of its evanescent nature, it is not ' 
surprising that the positron remamed 
undiscovered for so long Actually, 
after it had been identified, several 
scientists, looking through their files, 
found cloud-chamber photographs, due 
to cosmic rays, which indicated the 
presence of positrons There were 
probably extenuating circumstances 
to account for the failure to recognize 
them, nevertheless, Anderson must be 
commended, not only for his acute 
observation, but also for his coura- 
geous interpretation which solved a 
long-standing problem 

2 77. It may well be asked at this 
point what happens when a positron 
and an electron unite? It appears that 
the positive and negative charges neu- 
trahze each other and the particles are 
annihilated leaving only energy m the 
form of radiation, often called anniht- 
laiion radtaiion, similar to gamma rays 
(§ 2 104) The energy to be expected 
for this radiation can be calculated, 
and it is a striking fact that exactly 
such radiation was observed by J 
Thibaud and by F Johot, m 1933, 
when a stream of positrons was allowed 
to impinge on a metal surface The 
same radiations were also detected m 
other cases where positrons were pre- 


AUmxc Energy Chap II 

sumably annihilated by combining 
with electrons 

2.78 Before the identification of the 
positron, several physicists had found 
that the absorption of high-energy 
gamma rays by matter was appreci- 
ably greater than calculated from a 
well-established equation, which gave 
excellent agreement 'with experiment 
for rays of lower energy At the same 
time a secondary radiation, whose ori- 
gin could not be explamed, was de- 
tected m the United States by Chinese 
physicist C y Chao in 1930, and m 
England by L H Gray and G T P 
Tarrant m 1932 The interpretation of 
these results was provided by Blackett 
and Occhiahni Tlie additional absorp- 
tion of gamma rays was due to the 
conversion of their energy into posi- 
tron-clectron pairs, while the second- 
ary radiation had just the right energy 
to be expected for the aiuuhilation of 
the positrons as a result of combmation 
with the omnipresent electrons 

2 79 It has thus been clearly es- 
tablished that energy, m the form of 
gamma rays or cosmic rays, can be 
converted mto particle pairs, under 
suitable conditions, and, conversely, 
the pairs can combme to produce 
energy in the form of anmhilation radi- 
ation These results, as 'will be seen m 
Cliapter III, have an important bear- 
ing on the general principle of the re- 
lationship between matter and energy, 
a pnnciple upon which the reahzation 
of atomic energy is based 


X-RAYS 


The Discovert ane Nature 
OF X-Rays 

2 80 While expenmentmg with the 
luminescence produced by cathode 
rays, the German physicist, W 0 
Rontgen made a discovery, toward the 


end of 1895, which has had a notable 
effect, both direct and indirect, on 
atomic science It was stated earlier 
(§ 2 17) that the rays cause the glass 
walls of the discharge tube to lumi- 
nesce, but even more mtense lummes- 



47 


Conslituents of ihe Atom 


cence is produced in various chemical 
compounds, particularly barium plati- 
nocyanide, zinc blende (zinc sulfide) 
and willemite (zinc silicate). In the 
course of his work, Kontgen had en- 
closed a discharge tube in a box made 
of thin, black cardboard, placed in a 
darkened room. Near the tube there 
happened to be a sheet of paper coated 
on one side -with barium platinocya- 
nide, and Rontgen noticed that when 
the tube enclosed in the box was oper- 
ating the paper exhibited a brilliant 
luminescence. He proved that what- 
ever was responsible for this phenome- 
non originated in the vacuum tube, 
and he concluded that it was some 
form of penetrating rays, to which he 
gave the name of X-rays.* 

2.81. Eontgen found that in addition 
to producing luminescence, the rays 
caused darkening or fogging of photo- 
graphic plates, even when "wrapped in 
paper or enclosed in a box. Conse- 
quently, these substances, which are 
opaque to ordinary light, are trans- 
parent to the X-rays. This fact led 
Eontgen to take X-ray photographs of 
normally opaque bodies, such as the 
hand, thus revealing their internal 
structure due to the varying degrees of 
transparency of the different portions, 
c.g., bone and flesh, to the rays. 

2.82. To Eontgen goes credit for a 
discovcrj^ that might well have been 
made at any time during the two pre- 
ceding decades. William Crookes and 
F. Jerris Smith, in England, and, no 
doubt, others elsewhere, had found 
that photographic plates, although 
still in their unopened boxes, became 
fogged when kept in a room in which 
a discharge tube was in action. The 
phenomenon was usually attributed to 
some spurious external circumstances. 


and was not investigated. In addition, 
in 1890, A. W. Goodspeed, in Philadel- 
phia, actually produced shadow pho- 
tographs, which were really due to 
X-rays, but which he attributed to 
cathode rays; the Hungarian physicist 
P. Lenard obtained similar photo-, 
graphic results in 1894, using the so- 
called “Lenard rays” obtained by pass- 
ing cathode rays through an aluminum 
window in a discharge tube. 

2.83. In the early months of 1896, 
the investigation of the properties of 
X-rays attracted considerable atten- 
tion in .various parts of the world. 
Almost simultaneously, and independ- 
ently, scientists in England, France 
and Italy, found that when X-rays 
were passed through air, or other gas, 
the gas acquired the ability to conduct 
electricity. In other words, X-rays 
have the property of producing ions, 
i.e., electrically charged atoms or mole- 
cules (§ 2.15), in gases. There is little 
doubt that the experiments which re- 
sulted in this discovery were prompted 
by the photoelectric effect, well known 
at the time, whereby ultraviolet rays 
produce ionization in the air in the 
vicinity of a metal, such as zinc 
(§2.48). However, irrespective of its 
origin, it was a discovery destined to 
have a profound influence on atomic 
science. 

2.84. For several years after their 
discovery there was no clear under- 
standing of the nature of X-rays, and 
several different theories were pro- 
posed to account for their origin and 
behavior. It was not until 1912 that 
definite e\'idence, to be described in 
§ 2.88, was obtained that the rays 
were an electromagnetic radiation anal- 
ogous to light but of shorter wave 
length. 




50 


Sourcebook on Atomic Energy 


Chap II 


RADIOACTIVITY 


Discovery op Radioactivity 
2 92 Shortly after Rontgen'e an- 
nouncement of his discovery of X-rays, 
the French physicist Henn Antome 
Becquerel became interested m the 
subject as the result of a lecture given 
at the Academy of Sciences m Pans by 
H Poincar^ In answer to a question, 
the latter stated that the X-rays ap- 
peared to originate m the luminescent 
spot produced where the cathode rays 
impinge on the discharge tube Bec- 
querel s father, Edmond Becquerel, 
also a physicist, had made a particular 
study of a type of luminescence known 
as fluorescence,* exhibited by vanous 
substances, particularly upon exposure 
to sunlight Henn Becquerel happened 
to have in his possession a pure speci- 
men of the double salt, potassium 
uranyl sulfate, which hia father had 
used in his work on fluorescence In 
an attempt to discover some connec- 
tion between X-rays and the lumines- 
cence exhibited by this uranium salt.t 
Henn Becquerel ivTapped a photo- 
graphic plate in black paper, placed a 
thin crystal of the salt upon the paper, 
and then exposed the whole to sun- 
light When the photographic plate 
was dei^eJoped, it was found to be 
darkened, indicating that the uranium 
salt emitted radiations which could 
penetrate paper Becquerel showed 
that those rays could, m fact, pass 
through thm sheets of aluminum and 
copper and still cause blackening of the 
photographic plate At the time, be 
was of the opinion that the uranium 


salt had emitted the rays as a result of 
exposure to light, but, taking advan- 
tage of an unexpected circumstance, 
as mentioned below, he made a dis- 
covery which turned out to be of a 
revolutionary nature 
2 93 Describing his work, m the 
early part of 1896, Becquerel said, re- 
ferring to his experiments with the 
uranium salt placed over the photo- 
graphic plate wrapped in paper "Some 
had been prepared on Wednesday, 
February 26th and Thursday, Febru- 
aty 27th, but os on these days the sun 
shone only intermittently, I kept the 
experiments that had been prepared 
and returned the plates to the darkness 
of a drawer leaving the crystals 
of the uranium salt m place The sun 
not showing itself again the following 
days, I developed the photographic 
plates on March 1st, expectmg to find 
very faint images On the contrary, 
the silhouettes appeared with great 
intensity A hypothesis which 
occurs to the mmd will be to 
suppose that these radiations [emitted 
by the uranium salt] are similar 
to invisible rays emitted by phospho- 
rescent [fluorescent?] substances, ex- 
cept that the time of persistence is 
infoitely greater than that of the vis- 
ible radiations emitted by such bodies " 
TIius, Becquerel showed that the ura- 
nium salt emitted rays, even without 
bemg exposed to sunhght, and that 
these rays persisted for a long time 
In this manner was discovered the re- 
markable phenomenon to which Mane 


• The term fluorescence is generally used to deecnbe the emission of hght of a particular 
wave length as a result of exposure of a material to light of another — usually shorter — wave 
length the emitted light ceasing immediatdy the latter is cut off 

tH Becquerel desenbed this as phosphoreseence,’ a term which now generally refers to 
luminescence that continues for some time rfter the exatmg light is cut off, however, the 
uranium salt is probably fluorescent rather than phosphorescent 



51 


Conslituents of the Atom 


Curie, in 1898, gave the appropnate 
name of radioactivity (§ 5.5).* 

2.94. After Becquerel found that the 
radiations from uranium were similar 
to X-rays in the respect that they 
could penetrate materials opaque to 
ordinary light, and also affect a photo- 
graphic plate, he was naturally inter- 
ested to see if the radiations, like 
X-rays, were able to produce ionization 
in air. For this purpose he used a gold- 
Imf electroscope which, in its simplest 
foiTO, consists of a short, vertical metal 
rod with a metal sphere or plate at its 
upper end; to its lower end are at- 
tached two small rectangular sheets of 
gold leaf, hanging vertically. The rod 
is usually supported, with suitable 
insulation, in a box which serves to 
protect the delicate gold leaves from 



CHARGED DISCHARGED 


Fig. 2.9. Use of simple gold-leaf electro- 
scope to detect ionizing radiations. 

air currents. If an electric charge is 
applied to the sphere or plate, it is 
transferred through the metal to the 
gold leaves; since these both now carry 
charges of the same sign, they immedi- 
ately repel each other, forming an 
inverted V. (Fig. 2.9). If the air in the 
vicinity is ionized in some manner, it 
becomes an electrical conductor and 
thus permits the charge on the leaves 
to leak away. In other words, the 


electroscope becomes discharged. The 
repulsion then ceases and the leaves 
return to their original vertical posi- 
tions. Becquerel observed that a ura- 
nium salt brought near a charged elec- 
troscope caused the latter to discharge. 
Thus, the rays froni uranium had the 
property of ionizing the air in their 
vicinity. 

2.96. The subject of radioactivity 
will be discussed in some detail in later 
chapters and for the present purpose, 
which is a brief consideration of the 
nature of the emitted radiations, it 
is sufficient to state that Becquerel’s 
discovery was soon followed by the 
identification of other active elements, 
namely, thorium, polonium, radimn and 
actinimn, in which the French scien- 
tists Marie and Pierre Curie played 
an important part (Chapter V). At the 
present time, a considerable number of 
radioactive species are known; some 
occur in nature, while others are pro- 
duced by various transmutation and 
disintegration processes (Chapter XI). 

Radioactive Radiations: 

Alpha and Beta Rays 

2.96. It was observed ahnost simul- 
taneously in 1899 by Becquerel in 
France, by S. Meyer and E. von 
Schweidler and by F. Giesel in Ger- 
many, that the radiations from radio- 
active substances could be deflected in 
a magnetic field in the same direction 
as are cathode rays. It appeared there- 
fore that part, at least, of the radia- 
tions consisted of negatively charged 
particles. At about the same time, E. 
Rutherford (see § 2.64) was in England 


fioractimcffl made that the English phyKicist, S. P. Thompson, discoverec 
mdioacUvity almost simultaneously and independently of Becquerel. In 1896 Thompsoi 
^ photographic plate was covered with a thin sheet of metal, upon whicl 
^ immum wilt, and exposed to sunlight, the plate was affected. He ^Ued th( 
fwnSf "hvTcrphasphorescence." The essential point about radioactivity is that, a 

Thompson did not realize this. It may be men 
SI. ^^cto^, of France, reported that if a sSet of pane: 
tlm dm? esposed to light, it was able to affect a photograp^i 

1 . t in the dark, so as to cause cxccpbonally rapid reduction of the silver salt!irf;;ffie 'plate 



52 


SourcAook on Atomic Energy Chav H 


studying the extent to which passage 
through thin sheets of aluminum was 
able to reduce the ionizing power of the 
active radiations From his results he 
concluded that the radiations emitted 
by a uranium compound were of two 
different types one type, which Ruth- 
erford called alpha (o) rays, were un- 
able to penetrate more than about 
0 002 cm of alummum, while the sec- 
ond type, the beta (0) rays, required a 
much thicker sheet of alummum to 
absorb them completely The pene- 
trating po^^e^ of the beta rays was 
found to be \ ery roughly one hundred 
times that of the alpha rays 

2 97. The suggestion that there were 
two different kinds of rays was also 
made by Pierre Curie in 1900, when he 
found that part of the radiation from 
radioactive substances could be de- 
flected in a magnetic field whereas the 
other part appeared not to be deflected 
Evidently the latter was identical mth 
Rutherford’s alpha rays, because Mane 
Curie showed that they had a much 
smaller penetrating power than the 
beta rajs The latter are thus the 
radiations which are readily deflected 
in a magnetic field and, as E Dorn 
showed in 1900, also by an electnc 
fi^eld 

2 98 By collecting the rays in a 
Faraday cvhnder (§2 20), Mane and 
Pierre Curie m 1900 confirmed the fact, 
indicated by the deflections, that the 
beta rays were associated with a nega- 
tive charge It consequently appeared 
probable to Becquerel that the beta 
rays might be related to cathode rays, 
thus, in his own words “The experi- 
ments which I have made dunng the 
past several months on the radiations 
from radmra have showm that the 
properties of the part of this radiation 
which IS deviable in a magnetic field 
have a great analogy with those of 
cathode rays ’’ To demonstrate the 


complete identity of the beta and cath- 
ode rays, Becquerel (1900) detemimed 
both the speed and the charge-to-mass 
ratio I e , the specific charge, of the 
particles which presumably consti- 
tuted the beta rays, by studying their 
deflection in electnc and magnetic 
fields {§ 2 42 ef seg ) In this way, he 
found the velocity to bo about 1 6 X 
10“ cm per sec , which is just more 
than half the speed of bght, while the 
specific charge was approximately 3 X 
10‘^ e 3 u per gram These results, as 
Becquerel said, “are entirely of the 
order of magnitude which have been 
found for cathode rays ’’ Later work 
has established, with, complete cer- 
tainty, that beta rays do, in fact, hke 
cathode rays, consist of negatively 
charged electrons A beta particle is 
thus identical with an electron 

The Aipha Pasticle 
2 99. As stated above, early expen- 
ments mdicated that the alpha rays 
could not be deflected m a magnetic 
field, and hence appeared to be un- 
charged Nevertheless, some scientists, 
particularly R J Strutt (later Lord 
Rayleigh, 4th Baron) and W Crookes, 
m England, noting the strong ionizing 
power of the radiations, thought they 
might consist of positively charged 
particles of relatively large mass This 
view received confirmation from Ruth- 
erford when, in 1903, he succeeded in 
deflecting the alpha rays by using a 
powerful magnetic field, the direction 
of the deflection was opposite to that 
of an electron stream m the same field 
It was apparent, therefore, that the 
alpha rays actually consist of posi- 
tively charged particles 
2 100 Preliminary measurements of 
the specific charge (e/m) of alpha 
particles were made mdependently by 
Rutherford and by T Des Coudres m 
1903, by observing their deflections m 



53 


Constituents of the Atom 


magnetic and electric fields. The value 
so obtained was about 2 X 10*^ e.s.u. 
per gram, as compared wth 5.1 X 10^^ 
e.s.u. per gram for an electron. The 
former figure is of the same order of 
magnitude as for the atomic and 
molecular particles in positive rays 
(§ 2.G2), and so Rutherford concluded 
that "the alpha rays ... are thus 
very similar to the Kanalstrahlen [i.e., 
positive rays] . . . which have been 
shown ... to be positively charged 
bodies moving with high velocity." 
Shortly afterward, he said: “I have 
been ... led by a mass of indirect 
evidence to the view that the alpha 
rays are in reality charged bodies of 
mass of the order of that of the hydro- 
gen atom.” 

2.101. In 1906, Rutherford reported 
the results of more accurate measure- 
ments of e/m by deflecting the alpha 
particles, from several different radio- 
active sources, in both magnetic and 
electric fields.* The value found, 
1.5 X 10“ e.s.u. per gram, was about 
one half the value for a proton, i.e., for 
a hydrogen atom vdth a single electric 
charge (§2.64). TSvo reasonable in- 
terpretations of this result were pos- 
sible: first, the alpha particle might be 
a hydrogen molecule, having twee the 
mass of a hydrogen atom, but still 
carrjdng a single charge; and second, 
it might be a helium atom, with a mass 
four times that of a hydrogen atom, 
carrjdng two elementary charges. In 
either case, the e/m value would be 
approximately half that for a proton. 
Since both radium and actinium salts 
had been found to liberate helium, and 
this gas was knoum to be frequentlj’’ 
associated with radioactive minerals, 


Rutherford favored the second possibil- 
ity. He thought it probable, therefore, 
that alpha particles were helium atoms 
carrjdng two unit- positive charges; in 
other words, they were doubly charged 
helium ions or helium atoms each of 
which had lost two electrons. 

2.102. Partial confirmation of this 
view was obtained by E. Rutherford 
and H. Geiger in 1908, when they de- 
termined, by means of an electrometer, 
the total charge carried by the alpha 
particles emitted by a given radio- 
active source. Then the number of 
particles was counted, by methods to 
be described in Chapter VI, so that the 
charge on each alpha particle could be 
calculated. A somewhat similar pro- 
cedure was used by the German physi- 
cist E. Regener in 1909, and both sets 
of experiments led to essentially the 
same result. The charge on an alpha 
particle was found to be about 9.6 X 
lO-’” e.s.u., which is twice the value 
of the elementary electronic charge 
(§2.41). The alpha particle must thus 
carry two unit charges, and since its 
specific charge (e/m) is half that of a 
proton, its mass must inevitably be 
four times as great. The only reason- 
able particle of this mass is an atom of 
helium, so that the alpha particle 
should be represented by the symbol 
He++. 

2.103. In 1909, E. Rutherford and 
T. Royds provided a final, and un- 
equivocal, proof of the relationship 
between alpha particles and helium. 
A radioactive material, emitting alpha 
particles, w'as placed in a thin--vvalled, 
glass tube surrounded by a wider tube 
which had been evacuated. The alpha 
particles penetrated from the inner 


* The experiments vrcrc made in Montreal, Canada, but the paper in which they were de- 

Rutherford gave a course of lectured on radio- 
Tr t '' ® Umrcrsity of California, in the summer of 1906. It is of interest to record 

w that part of the work was done ^rith the assistance of 0. Hahn, who wS Zre S 

£ira wwll part in connecdon with the discoverj^ of nucleir 

luaon vhich made possible the utilization of atomic energy (§ 13.7), ^ 



54 Sourcebooh on 

into the outer tube, through the thin 
glass walls After several days, an 
clectnc discharge was passed throu^ 
the outer tube, when it showed the 
unmistakable spectrum of helium gas 
This could only have come from the 
alpha particles, and so it must be re- 
garded as definitely estabhshed that 
these particles are doubly charged he- 
lium ions, 1 e , helium atoms carrymg 
two unit positive charges By pickmg 
up two electrons, an alpha particle 
eventually becomes an ordmaiy (neu- 
tral) helium atom 

Gaiima. Rays 

2 104. A third type of radiation, 
which could not be deflected m a mag- 
netic field but which nevertheless had 
considerable penetrating power and a 
marked effect on a photographic plate, 
was discovered by P Villard m France 
m 1900 These radiations are now 
called gamma (y) rays * As with cath- 
ode rays, the nature of the gamma rays 
was at first the subject of controversy 
F Paschen and W K Bragg thought 
they were high-speed particles, whereas 
C G Barkla and E Rutherford 
favored the view that they were of a 
wave nature similar to X-rays Defi- 
nite proof of the correctness of the 
latter view was obtained by E Ruther- 
ford and A N da C Andrade in 1914 
when they succeeded m causing the dif- 
fraction of the gamma rays by means 
of a suitable crystal (§ 2 87) Direct 
measurement of the wave lengths of 
the rays in this maimer gave values 
corresponding to those for very short 
X-rays The gamma rays, like X-rays 
and light rays, are thus a form of elec- 
tromagnetic radiation (§ 3 23) 


Atomic Energy Chap 11 

CoMPAKiBON OP Radiations 
2 106 In reviewing the properties of 
the three types of radioactive rays, it 
may be said that the alpha rays have a 
very weak penetrating power, being 
completely absorbed by a few sheets of 
paper These rays, however, are able 
to produce marked ionization of gases 
through which they pass, partly be- 
cause of their relatively large mass and 
hi^ velocity The beta rays are much 
naore penetrating than the alpha rays, 
some millimeters of aluminum being 
required to absorb them, but their 
lomzmg power is appreciably less Fi- 
nally, the gamma rays are highly jiene- 
trJitmg, several centimeters of lead 
may sometimes fail to cut them off 
completely, although they produce rel- 
atively little ionization m their path 
through air 

2 106 All three types of radiation 
can affect a photographic plate m the 
dark It is of interest to recall that the 
initial discovery of radioactivity by 
Bocquerel was due to the photographic 
action of the radiations from uranium 



FiO 2 10 Mane Cune’s representation 
of alpha beta and gamma rays m a mag- 
netic field 

The differing electrical properties of 
th^ radiations are summanzed m the 
form of a diagram (Fig 2 10) which 
Mnne Cune included in her doctorate 


* It has been stated that VjUard gave tiua name to the rays, but such does not appear to 
be the case The term gamma rays came into general use m 1903, although it is not certam who 
originated it The present writer is of the opinion that it was Rutherford, but there is a possi- 
bility that Becquerel was responsible 



55 


Constituents 

Thesis, published in 190S. It is sup- 
posed that a radioactive material is 
placed in a narrow but deep cavity in a 
block of lead, so that, in the absence 
of electric and magnetic fields, the 
rays would emerge as a narrow vertical 
beam. However, if a strong magnetic 
field were applied in a direction per- 
pendicular to and into the plane of the 
paper, the alpha particles, being posi- 
tively charged and relatively heavy, 
would be slightly deflected to the right, 
the beta particles, since they are nega- 
tively charged and light, would be 
deviated to a greater extent to the 
left, while the gamma rays, carrying 
no electric charge, would not be de- 
flected at all. 

2.107. Most naturally occurring ra- 
dioactive elements radiate either alpha 
or beta particles, althou^ in a few ex- 
ceptional instances both are emitted.* 
In some cases, gamma rays accompany j 
the alpha or beta particles. The essen- 
tial nature of the rays is the same, 


of the Atom 

irrespective of their origin; the alpha 
particles are always doubly-charged 
helium, atoms, the beta particles are 
electrons, and the gamma rays are 
electromagnetic waves. However, the 
specific properties of the radiations, 
such as the velocities of the alpha and 
beta particles, their penetrabilities and 
power of ionizing gases, and the wave 
lengths of the gamma rays, depend on 
the particular radioactive element irom 
which they originate. 

2.108. The foregoing description of 
the radiations .has referred in particu- 
lar to those obtained from naturally 
occurring radioactive elements. In re- 
cent years a much larger number of 
active elements have been obtained in 
what might be called an artificial man- 
ner (Chapter XII), Some of these 
“artificially” radioactive elements, es- 
pecially those of high atomic weight, 
emit alpha particles, while others expel 
either electrons or positrons (§ 2.71), 
together with gamma rays. 


THE NEUTRON 


Prediction of the Neutron 

2.109. In the year 1920 there ap- 
peared, from tluree widely separated 
sources, the suggestion that an entirely 
new and hitherto undiscovered par- 
ticle, might be an important unit in the 
structure of atoms. The particle of 
which the possible existence was con- 
sidered bj’’ W. D, Harkins in the 
United States, by Orme Masson in 
Australia, and by E. Rutherford in 
England, was believed to result from 
the neutralization of the electric charge 
of a proton by an electron, leaving a 


neutral, i.e., uncharged, particle, hav- 
ing a mass of unity, on the ordinary 
atomic weight scale.f In his Bakerian 
Lecture to the Royal Society in 1920, 
Rutherford said: “Under some con- 
ditions ... it may be possible for an 
electron to combine much more closely 
with the hydrogen nucleus [i.e., a 
proton], forming a kind of neutral 
doublet. Such an atom would have 
novel properties. Its external field 
Avpuld be practically zero . . , and 
consequently it should be able to move 
freely through matter. Its presence 


1 he emission of bofli alpha and beta particles by uranium salts, as observed by the earlv 
V^’ presence of other active elements in addition to uranium (see 

^ ^ former collaborator B. B. Boltwood of Yale 


conremmg the particle of Unit mass and zero 
f: • • * most of the ideas . « • have been common prooertv in thr? mimfrv 

li.e., EriElnndJ and especially to myself for the last five 3'eare.’’ 



56 Sourcebook on Atomic Energy Chap IX 

would probably be difficult to detect” penetrating radiation was obtained 
This hypothetical particle, to which It was thou^t that this might be a 
was given the name neufron,* was des' form of gamma ray of high energy 
tincd to play a totally unexpected role, "While repeating these experiments in 
not only in the history of atomic sci- 1932, I Joliot-Curie and P Joliot 
ence but also in the fate of nations (| 2 75) found that when a sheet of a 

2 110 Since the neutron was re- hydrogen-containing material, partic- 
gardcd as a close combination of a ularly paraffin, was mterposed m the 
proton, 1 e , a gaseous hydrogen ion, path of the new radiation, protons were 
and an electron numerous unsuccessful ejected wth a considerable velocity 
attempts were made m Rutherford’s Tlie Joliots thought they had dis- 
laboratory, and probably elsewhere, to covered a “new mode of interaction of 
detect the formation of neutrons by radiation with matter” whereby clec- 
the passage of an electric discharge tromagnetic waves were able to im- 
through hydrogen Rutherford also part large amounts of kinetic energy, 
reported that he and his assistant, i e , energy of motion, and momentum 
James Chadwick, who finally identi- to light atoms The results were, how- 
fied the neutron some years later ever, not m accord with the require- 
(§2112), had attempted to obtam ment of the accepted laws of mechanics, 
neutrons by bombarding aluminum and so there arose a dilemma either 
ivith fast alpha particles from a radio- the usual mechanical laws did not hold 
active source, these efforts, too, met m this instance, or the so-called radLh 
with failure, although, as later events ation was not of an electromcgnetic 
proved, the experiments were actually nature analogous to gamma rays 
on the nglit lines In September 1924, 2112. The situation was resolved by 

Chadiviok wrote to Rutherford, who James Chadwick, m England, m 1932 
■n as then on a visit to the Umted Referring to the observations of Both© 
States “I think we shall have to make and Becker, of the Johots and also of 
a real search for the neutron I believe H C Webster, made at about the 
I have a scheme which may just work same time, he said “The experimental 
but I must consult Aston first ” But, if results are very difficult to explam on 
the scheme ^ as tried, it was evidently the hypothesis that the beryllium radi- 
not successful ation was a quantum [i e , electromag- 

netic] iwha^on, but followed imme- 
Discovery op the Neutron diately if it were supposed that the 

2 111. The actual discovery of the radiation consisted of particles of mass 
neutron came as an unexpected cul- nearly equal to that of the proton and 
mmation of a senes of events In 1930, with no net charge ” In other words, 
W Bothe and H Becker reported from by supposing that the apparent new 
Germany that if certam light elements, radiation was really a stream of neu- 
notably beryllium and to a lesser ex- trons, which have a particle nature but 
tent boron and lithium, were exposed no charge, the observed facts could be 
to alpha rays from the natural radio- interpreted without the necessity of 
active element polonium, a very highly discardmg the laws of mechames It is 

• The «ord neutron was apparently first employed in this connection by W D Harkmsin 
1921, thus “neutron a term representing one negative electron and one hydrogen nucleus 

h e , a proton] ” 



57 


Constituents of the Atom 


easy to understand how a fast-moving 
particle like a neutron can impart ki- 
netic energj’’ and momentmn to a hy- 
drogen or other light atom. Bj’’ attrib- 
uting to the new particle a mass of 
unity, on the atomic weight scale, 
Chad^Yick showed that the results of 
the earlier experimenters could be com- 
pletely explained.* 

2.113. Since the neutron carries no 
electric charge, it produces no appreci- 
able ionization in its path and hence 
gives no visible track in a cloud cham- 
ber (§§ 2.67, 6.50). This is one expla- 
nation of why it proved difficult to 
detect. On the other hand, the absence 


of charge accounts for its very high 
penetrating power for reasons which 
will become apparent after the nature 
of the interior of the atom has been 
discussed (Chapter IV). 

2.114. In the years since 1932, Chad- 
wick’s identification of the neutron has 
been amply verified in laboratories the 
world over. A number of different 
ways of producing neutrons have been 
discovered, and it is now kno^vn that 
these particles are fundamental units 
of atomic structure. In view of its 
great importance, the neutron merits a 
much more detailed treatment, and 
this will be given in Chapter XI. 


* F. Joliot is reported to have stated — after Chadwick’s explanation of their observations — 
that if he and his wife (I. Joliot-Curie) had read Rutherford’s 1920 Bakerian Lecture, in which 
the possible existence of a neutral particle of unit mass had been eonsidered (§ 2.109), they 
would probably have identified the neutron themselves. 



Energy and Eadiatim Chapter III 


THE NATURE OF ENERGY 


Forms of Energy 
3 1, Although the study of enei^* 
IS one of the most important aspects 
of physical science, it is difficult to 
supply a precise definition in simple 
language Broadly, it may be stated 
that energy is work, or anythmg that 
can be converted into work But this 
statement, obviously, has no meaning 
wthout an explanation of the signifi- 
cance of work, and for the present 
purpose it is sufficient to say that 
work la done whenever there is a move' 
ment of a body or particle against a 
resisting force In general, therefore 
energy has the capacity of causing the 
motion of a body in spite of the opera 
tion of a force resisting the motion 
The expenditure of energy in this 
manner may result in its conversion 
mto heat, as, for example, when two 
bodies are moved relative to one an- 
other agamst the force of friction 
3 2 Energy can take many forms, 
several of which are easily converted 
into one another, and all of which can 
be used, at least in prmciple, to per- 
form some kind of work This work is 
not necessarily obtamed in a useful 
form, but the definition is satisfied in 
the respect that there is motion agamst 
a force Coal or oil, together inth oxy- 
gen from the air, contains energy 
which appears as heat when, the fuel 
is burned m a boiler The heat energy 
may then be used to raise the temper- 
• Prom the Greek, en (in) and ergon (work) 


ature of water to produce steam, the 
molecules of the latter, possessing more 
energy than the molecules of cold 
water Then the energy of the steam 
can be converted into mechamcal en- 
ergy, as m a steam engme, which 
may be used to drive a ship or a tram 
against the resisting force of fnction 
due to the water or to the rails and 
air, as the case may be Alternatively, 
the mechanical energy can be changed 
mto electneal energy m a dynamo, 
and back again mto mechanical energy 
m an electric motor 
3 3 Atomic energy is a form of en 
ergy that is not essentially different 
from the forms described above When 
an oil, which is a hydrocarbon or com 
pound of hydrogen and carbon, bums 
in tlie oxygen of the air, there is a lib- 
eration of energy due to a chemical 
reaction resultmg m the formation of 
water and carbon dioxide In other 
words, energy is produced as a conse 
quence of a rearrangement of the atoms 
of hydrogen, carbon and oxygen tak- 
ing part m the reaction Atomic en 
eigy, on the other hand, results from 
rearrangements within the interior of 
the atom itself Once the release of the 
atomic energy is achieved in a siutable 
manner, it might, m pnnciple if not m 
practice, be used for performing work 
34 Whenever a large amount of 
energy is liberated within a very short 
mterval of time, the result is an explo- 



69 


Energy and Radiation 


Bion, The operation of the engine of 
an automobile or of an airplane de- 
pends on the explosions occurring in 
the cylinder when a spark is passed 
through a mixture of gasoline (h 3 ^dro- 
carbon) vapor and atmospheric oxy- 
gen. However, if gasoline is burned in 
the open air, the release of energy takes 
place more slowly and there is no ex- 
plosion. The heat of the flame could 
be used to produce steam and this 
could be made to run a steam engine. 
In a general way, the same is true of 
atomic energy. The very sudden re- 
lease of a tremendous amount of en- 
ergy, in the so-eaUed atomic bomb, 
leads to a powerful and devastating 
explosion. But it is possible to liberate 
the energj'^ gradually so that it may be 
employed to do useful work. The way 
in which this application of atomic 
energj’’ might be achieved will be 
considered in Chapter XIV. 


3.6. Every form of energy can be 
regarded as kinetic energy, or ‘potential 
energy, or both. The kinetic energy of 
a body or particle is energy of motion, 
■while potential energy is that of posi- 
tion, relative to other bodies, or condi- 
tion. Potential energy can usually be 
readily converted into kinetic energy. 
For example, the water at rest behind 
a dam has potential energy but if it 
overflows, its potential energy is con- 
verted into kinetic energy of motion. 
Ordinary fuels and certain atoms pos- 
sess potential energy which can be 
changed into kinetic energy by suit- 
able means. The kinetic energy of a 
body is determined by its mass m and 
its velocity of motion v, the actual 
value being When the tem- 

perature of a substance is raised, by 
supplying heat, the molecules move 
more rapidly, and hence their kinetic 
energy increases. 


THE NATURE OF RADIATION 


RA-DIANT ENEHOy 

3.6. Radiant energy, or radiation, is 
of great importance in various atomic 
studies, and hence the subject merits 
fairly detailed consideration. It is the 
form in which energj'- can be transferred 
from one point to another through 
space. Two veiy familiar, but appar- 
ently different, kinds of radiation are 
light and radio waves. The sun’s en- 
which incidentally is a type of 
atomic cnergj’ (§ 14.143), is conve 3 'ed 
to the earth largely in the form of 
light, or visible radiation jis it is sorac- 
time.s called. Vflien it reaches the 
earth’s surface, the energ 3 ' of the sun- 
light is either alxsorbed 1 ) 3 '' gi'een plants 
anil stored a,H chemical (potential) en- 
ergy, m.ainly in carbohydrates such as 


sugars and starches, or it is converted 
into heat which warms the atmosphere 
(kinetic energy). In a somewhat re- 
lated manner, small amounts of energy 
are transferred from a radio transmit- 
ter to a distant receiver in the form of 
radiation. This radiation, however, is 
not visible, that is to sa 3 '', it does not 
affect the eye in the same manner as 
does light. Other forms of invisible 
radiations are ultraviolet light, X-rays 
and gamma ra 3 '^s.* 

3.7. Since all kinds of radiation are 
fundamentally the same, it iidll be 
convenient to discuss first what is per- 
haps the most familiar form, namel 3 '^, 
light. The concept that light consists 
of particles projected from luminous 
bodies into the e 3 ''e of the obserymr was 


arc aho sometimes referreti to as “radiations”: thev are howevr 
.idmtions in the sense of radiant energj- or electromagnetic radiation considered her 



60 


Sourcebook on 

proposed by the philosophical school 
of Pythagoras, around 500 B C This 
idea was revived in the latter part irf 
the seventeenth century by the Eng- 
lish mathematician Isaac Ne« ton He 
considered the best way to explain the 
fact that h^t travels m straight lines 
and casts sharp shadows was to sup- 
pose it to be made up of small particles 
or corpuscles An alternative theory, 
that light IS a form of undulation or 
wave motion, was proposed in a vague 
form by Robert Hooke in England, 
and its consequences were worked out 
in some detail, about 1680, by Chris- 
tian Huygens, the noted Dutch au- 
thority on optics But Newton was 
opposed to the wave theory because it 
seemed to him that it could explam 
neither the formation of sharp shadows 
nor certain other optical effects known 
at the time 

The 'Wave Theory of Light 

8 8 For over a hundred years the 
corpuscular structure of light was 
widely accepted, but, m the early 
1800s, Thomas Young, m England, 
and Augustin Jean Fresnel, m France, 
revived the wave theory and showed 
how Newton’s objections could be 
overcome The sharpness of shadows, 
for example, could be accounted for 
by the extreme smallne*^ of the light 
waves, so that the abihty to turn cor- 
ners, normally possessed by waves, 
was undetectable in the ordinary way 
Nevertheless, careful study of the be- 
havior of light as it passes by the sharp 
edge of an opaque body or throu^ a 
very narrow slit, shows that it is actu- 
ally bent and spread out from its hnear 
path, as IS to be expected for a wave 
motion This is an aspect of the phe- 
nomenon known as di^raclion of h^t 
(cf §2 87) 

3 9 The facts of optical interference 
also appear to require the existence of 


Atomic Energy Chop III 

light waves to provide an adequate 
explanation If homogeneous light 
from a given source passes throu^ a 
number of narrow shts very close to- 
gether, and the emergent rays are al- 
lowed to fall on a screen, the result 
will not be an equal number of thm 
etnps of light, as might ha\ e been ex- 
pected, but a senes of hght and dark 
bands This is referred to as an inter- 
ference pattern, or diffraction ■pattern 
I 3.10 The explanation based on the 
I wave theory is that the hght is dif- 
I fracted, that is to say, it is bent out of 
I Its path, and spread out somewhat, m 


SCREEN 



Fic 3 1 Diagrammatic representation of 
a diffraction grating w ith light \\ aves pass- 
ing through ehts 


passing through the small shts If, at 
a certain point m the screen, two rays 
of h^t commg from the shts are m 
phase, 1 e , if the crests of one set of 
waves coincide exactly with the crests 
m the other set, the two rays will rem- 
force one another giving a stnp of in- 
creased brightness At an adjacent 
pomt, however, the two rays wiU be 
out of phase, the crests m one ray co- 
inciding with the troughs m the other, 
the two rays will thus tend to annul or 
interfere with one another, so that 
there is a strip of virtual darkness 
(Fig 3 1) The same general behavior 
^ould occur at a senes of points, thus 
giving rise to a pattern of successive 
hght and dark bands, as actually ob- 



61 


Energy and Radiation 


served. TWule s. s£itisf3.ctory interpre“ 
tation. of interference effects is possible 
in terms of the wave concept, the cor- 
puscular theory fails to offer any rea- 
sonable alternative. It should be noted 
that in order to obtain satisfactory 
interference effects, the slits should be 
narrow and their distance apart must 
be of the same order as the wave length 
of light, i.e., about 5 X 10"^ cm. 
(§ 3.16). An arrangement of this kind 
for producing a diffraction pattern is 
Itnown as a diffraction grating, because 
its structure is similar to that of a 
grating, but on a very small scale. 

3.11. By the middle of the nine- 
teenth century, moderately accurate 
measurements of the velocity, or speed, 
with which light travels from one point 
to another had been made, cliiefly by 
A. H. L. Fizeau and by J. B. L. Fou- 
cault in France. This work provided a 
crucial test of the two rival theories 
concerning the nature of light. Ac- 
cording to the wave concept, the speed 
should be greater in air than in a more 
dense medium like water, but the 
Newtonian corpuscular theory required 
the reverse to be the case. The results 
showed that the former was actually 
true, thereby providing further sup- 
port for the wave theory of light. 

The Natuhe of Wave Motion 

3.12. At this point an attempt must 
be made to consider the character of 
wave motion in general, and of the 
particular type that is involved in 
light. If a small stone is dropped verti- 
cally in the center of a pool of Avater, a 
.‘•cries of ripples or waves will be seen 
to move outAvard in concentric circles. 
However, a cork floating on the sur- 
face of the Avater Avill not moAm out 
with the AvaATS, but aatII merelj*^ bob 


up and down as each Avave crest and 
trough, respectively, passes it by. It 
is clear, therefore, that although the 
AA'ater acts as a medium in which the 
AA'aves can move aivay from the center 
of disturbance,- the water itself does 
not travel in the direction of propaga- 
tion of the waves, but only at right 
angles to it. A Avave motion of this 



Fig. 3.2. TransA’^erse wave motion; the 
motion of the medium is at right angles 
to the direction of propagation of the wave. 

kind is said to be transverse, since the 
direction of motion of the medium is 
transverse to, or across, that in AA^hich 
the Avaves are being propagated (Fig. 
3.2). Various studies shoAV that light 
has the character of such a transverse 
Ava\m motion, although there is no ac- 
tual up and doAvn movement of the 
medium, e.g., air or Avater, through 
Avhich the light travels.* 



3.13. A AvaA'e motion consists of a 
series of crests and troughs, as seen in 
Fig. 3.3; the distance betAA^een anj' tivo 
successum crests, or successive troughs, 


till prop-tgated tus waves, but these arc longitudinal i 

viaw h direction m which tl 



62 


Sourcebook on Atomic Energy 


IS kno^Ti as the loave length, and is usu- 
ally represented by the Greek letter 
lambda, X In general, X is the linear 
distance from any position on one 
wave to the corresponding position on 
the next wave Suppose the wa\ emo- 
tion IS propagated with a velocity c 
expressed, for example, on centimeters 
per second, and suppose further, that 
the wave length X la also given m centi- 
meters The number of waves passing 
a certain pomt m the medium in the 
course of one second will then be equal 
to c/X This quantity is called Hie fre- 
quency of the wave motion and is rep- 
resented by the symbol v (Greek, nu), 
so that it is possiblp to write the im- 
portant equation 

V = ^ or X = ^ (31) 

giving the relationship among the wave 
length X, the frequency v, and c, the 
speed, or velocity of propagation of 
any wave motion, including light * 

The Speed op Light 
3 14. As imphed earlier, the speed 
of light, as with other wave motion, 
depends on the medium through nhich 
it passes The value usually recorded 
for light IS that for empty space, i e , 
for a perfect vacuum Actually, meas- 
urements are made in air and a small 
correction is applied In view of the 
tremendously lugh velocity with which 
hght is propagated, about 186,000 
miles per second, the measurement of 
the speed of hght is difficult Never- 
theless, several highly accurate proce- 
dures have been developed for the 
purpose, so that the value is now known 


Chap III 
with a considerable degree of precision 
This IS indeed fortunate as the speed 
of light in empty space is one of the 
fundamental constants of nature For 
scientific work it is usual to state the 
speed in centimeters per second, and 
this is 2 99776 X 10'“ cm per sec 
However, for most purposes it is suffi- 
cient to round the value off to 3 00 X 
10'“ cm per sec , which will be used 
throughout this book t 
3 IB. In the foregoing discussion the 
I term “light” has been used m a general 
I sense without specifying any particular 
I color The reason is that experiment 
has shown that all forms of light travel 
m empty space with exactly the same 
speed In this connection, therefore, 
the color of the light is immatenal 
What, then, is responsible for the dif- 
ferent possible colors which hght 
manifests? Variations of color are 
now known to be due to differences m 
the wave length of the hght Since the 
speed of propagation is aluays the 
same, it may equally nell be stated 
that color differentiation is attributed 
to frequency differences 

Color akd Wave Length 
3 16 As Newton first showed, white 
light is actually a mixture of all the 
visible colors, i e , all the colors to 
which the normal eye is sensitive, they 
are essentially red, orange yellow, 
green, blue, mdigo and violet — the 
colors of the rainbow Of this senes, 
red h^ the longest and violet the short- 
est wave length, the values being ap- 
proximately 7 60 X 10"® cm and 3 85 
X 10"® cm , respectively The wave 
lengtl^ of the other colors occupy in- 
termediate positions in the order given 


* A quantity, known as the wave number, which is equal to the reciprocal of the wave 
length, 1 e , l/x, is commonly used in spectroscopic work The wave number is the ni^ber 
of waves m a centimeter length, and is equal to the frequency of the waves divided by the 
velocity of light. , ... 

t The factor 3 X lO*® referred to in the first footnote in § 2 43 for the conversion of electro- 
magnetic to electrostatic units of charge is the velofsly of light 



63 


Energy and Radiation 


Quite frequently, wave lengt^ of light 
are quoted in terms of the Angstrom 
\mit (A), which, as stated in § 1.68, is 
equal to lO"* cm.; the wave lengths of 
visible light fall within the range of 
7600 to 3850 A. 

3.17. It was seen in Chapter I that 
atomic diameters are usually around 
2X10"® cm., that is, about 2 A; con- 
sequently, the wave lengths of light 
waves, although quite short from the 
ordinary standpoint, are still two or 
three thousand times the diameter of 
an average atom. The smallest parti- 
cle that can possiblj^ be seen in an ordi- 
narj’’ optical microscope must have 
dimensions of the same order as the 
wave length of the light used. It is 
evident therefore that an atom or mol- 
ecule is too small to be seen in such a 
microscope. A cube consisting of two 
or three thousand atoms in each of 
three directions, and thus containing 
a total of several billion atoms, would 
be just visible. 

3.18, It is well knovm that photo- 
grapliic plates or films are sensitive to 
light, but all colors do not affect them 
equally. Most ordinary film is hardly 
affected by red light, so that a mbj'^ 
lamp is often used in the so-called 
“dark room.” By adding certain chem- 
ical substances to the photographic 
emulsion, the film can be rendered 
sensitive to red light, and even to radi- 
ations of longer wave length which are 
invisible to the eye. These are the 
tnfrarai ray.^ emitted to a greater or 
lesser extent by most substances under 
normal conditions. A hot body emits 
more infrared radiation than does a 
cold one. It is the presence of these 
infrared rays, in conjunction with spe- 
ci.aUy prepared film, that makes it 
ptxssible to obtain photographs through 
fog or even in the dark. It is not in- 
tended to consider this subject further 
hem, except to erapluasiEo the fact that 


radiations exist which are completely 
invisible to the human eye. There is 
no essential difference betw’een infra- 
red rays and visible light, except that 
the former^have wave lengths greater 
than 7600 A, the normal upper limit of 
visibility. 

3.19. The lower limit of visibility is 
represented by violet light, with a 
wave length of about 3850 A. Never- 
theless, the existence of radiations of 
shorter wave length can be readily 
proved; these are the ultraviolet rays 
present to some extent in summer sun- 
light, especially in the upper atmos- 
phere, and also in many electric dis- 
charges such as arcs and sparks. Ordi- 
nary photographic film is extremely 
sensitive to ultraviolet radiation, al- 
though the latter is quite invisible to 
the human eye. By means of special 
instruments the wave lengths of ultra- 
violet rays have been measured down 
to about 1000 A. 

Electromagnetic Waves 

3.20. At this point it may well be 
asked: If there are radiations having 
wave lengths both longer and shorter 
than %dsible light, may there not be 
raj^s that are still longer and shorter, 
respectivelj’-, than those in the infrared 
and ultraviolet regions? The answer 
to this question is that such radiations 
are knoxra. They include the great 
range of radio waves, from radar to 
long-wave radio, at the one extreme, 
and gamma rays and X-rays, at the 
other axtreme. These radiations are 
fundamentallj'- the same; they all 
travel with the same speed — ^the speed 
of light — and differ onlj-^ in the length 
of their waves, covering the enormous 
range from about 10-^“ cm. for gamma 
rays to 10® cm. for the longest known 
radio waves. 

3.21. In the eaiij’- years of the nine- 
teenth century, AI. Faraday (see § 2.7) 



C6 

found to hold only at low tempera- 
tures or for short wave lengths, while 
that of the latter nas applicable taily 
at high temperatures or for long wave 
lengths The dilemma was resolved m 
1900, m a completely revolutionary 
manner, by the German physicist Max 
Planck Both Wien and Rayleigh 
thought of the black body as consistmg 
of a system of vibrators oscillating at a 
particular frequency corresponding to 
the frequency of the absorbed or emit- 
ted radiation The radiation, which 
was regarded as navehke in nature, 
was considered to be absorbed or 
emitted m a continuous manner 

3 29 While retaining the general 
concept of oscillators, Planck discarded 
theidea that energy can be contmuously 
absorbed or emitted Ho su^sted 
that a body absorbs or emits enejgy m 
the form of radiation in integral multi- 
ples of a definite amount or quantum,* 
the magmtudo of which depends on the 
vibrational frequency of the oscillator 
In other words, the energy of a body is 
not contmuously variable, but must 
consist of a specific whole number of 
quanta, the energy can be taken up or 
given out in such quanta only A body 
can thus emit or absorb one, two, three, 
four, etc , quanta of energy, but no 
intermediate or fractional amounts 
This statement forms the basis of the 
quantum theory of radiation, a theory 
which has found application m many 
areas of science 

3 30. According to Planck, the quan- 
tum E of energy for radiation of fre- 
quency vf is given by the simple, but 
fundamental, expression 


C/icp UJ 
E = hv, (32) 

where A is a universal constant, usually 
known as the Planck constant The 
energy quantum for a particular radi- 
ation IS thus directly proportional to 
its frequency By equation (3 1), the 
frequencj varies inversely as the wave 
len^h, hence, the magnitude of the 
enei^ quantum is inversely propor- 
tional to the wave length of the radia- 
tion The quantum for gamma rays, 
for example, is consequently relatively 
large, whereas for radio waves it is 
very considerably smaller The exact 
relationship between the energy quan- 
j turn and the wave length X of the radi- 
j ation may be obtained by combining 
equations (3 1) and (3 2) giving, 

(3 3) 

where c is the velocity of light 
3 31. Making use of equation (3 3), 
and the postulate that oscillators take 
up or give out energy m terms of whole 
numbers of quanta, Planck was able to 
derive an expression for the variation 
with the wave length of the energy 
radiated by a black body that was m 
complete agreement with experiment 
at all reasonable temperatures and 
wave lengths Further, for radiations 
of long wave length or for high tem- 
peratures, Planck^B equation reduces 
to that of Lord Rayleigh, whereas for 
short wave length or for low tempera- 
tures it becomes identical with the one 
proposed by Wien Thus, the quantum 
theory was shown to be superior to the 


Souredmoh on Atomic Energy 


* Planck onginally referred to these definite quantities of energy as "energy elements ” 
The term "energy quantum’ was introduced laker, {wobablv by A Einstein in 1905 (see §3 34) 
t In his treatment, Planck defined y as the frequency of the o«ieillator absorbing or emitting 
the radiation Since the radiation has the same frequency as the oscillator, it is less confusing 
and equally satisfactory for the present purpose, to take v as the frequency of the radiation 



67 


'Energy and Radiation 


previous attempts at treating the ab- 
sorption and emission of radiation; 
this was to prove to be the first of its 
many achievements. 

3.32. The magnitude of the Planck 
constant h, which is one of the funda- 
mental constants of nature whose sig- 
nificance is not yet coinpletely under- 
stood, has been determined in several 
ways. If the measurements are ex- 
pressed in terms of the centimeter- 
grara-second, or c.g.s., system, where 
distance is measured in centimeters, 
mass in grams and time in seconds, the 
energ}’’ unit is the erg.* The experi- 
mental value of h is then 6.62 X 10“^ 
erg sec., with the frequency v in vibra- 
tions per sec., or the wave length X in 
cm. Thus, by equation (3.2), 

E (ergs) = 6.62 X per sec., (3.4) 

and by equation (3.3), taking c, the 
velocity of light, as 3.00 X 10'® cm. 
per sec., 


E (ergs) = 


6.62 X 10-2' X 3.00 X 10»® 


X cm. 


1.99 X 10-'® 
X cm. 


For a gamma ray, for example, with a 
wave length of 10“'® cm., the quantum 
is 1.99 X 10~® erg; for a long radio 
wave, with X equal to 10® cm., the 
quantum is 1.99 X lO"^^ erg. 

The Photon 

3.33. It should be made clear that 
Planck’s thcon,’^ referred only to the 


taking up or giving out of radiation in 
terms of an integral number of energy 
quanta. The propagation of the radia- 
tion through space was still regarded 
as a wave motion, as described earlier. 
However, this point of view began to 
encounter some difficulties. It was 
mentioned in § 2.83 that X-rays are 
able to cause ionization of a gas 
through which they pass; in other 
words, the X-rays eject electrons from 
the atoms or molecules of the gas. But 
the number of ions formed is not large, 
considering the energy of the radiation. 
If the X-rays are waves spreading in 
all directions, it might be anticipated 
that electrons wmuld be removed from 
all molecules or atoms over which the 
rays passed, instead of from a select 
few. This discrepancy was difficult to 
explain. Further, in 1902, P. Lenard 
(see § 2.82) had found, when studying 
the emission of electrons from metals 
by the photoelectric effect (§2.49), 
that the energy of the electrons is 
independent of the intensity of the 
radiation employed to produce them. 
An attempt to explain these observa- 
tions was made by J. J. Thomson by 
means of a modified form of the wave 
theory, but this proved to be not too 
satisfactory. 

3.34. A solution of the problem was 
found in 1905 by Albert Einstein (see 
§ 3.64), w'hose development of the 
theory of relativity was later to pro- 
\ide the basic atomic energy equation 
(§ 3.71). He suggested that not merely 
w’^as radiation absorbed and emitted in 
w'hble numbers of energy quanta, as 
Planck had proposed, but also that it 


• An ere h the work done when a force of 1 djTie acts through a distance of 1 cm The 

^ ^ ^ acceleration of 1 cm. per sec. 



68 


jSrotirc€6ooJb on 

was actually propagated through space | 
m definite quanta or photons,* moving | 
with the speed of light This surprismg | 
view, which apparently discarded the 
wave theory of light in favor of some- 
thing very much akin to a particle 
concept, supplied a complete inter- 
pretation of the known photoelectric 
phenomena The equations derived by 
Einstein proved to be correct in all de- 
tails, so that the idea of radiation being 
transmitted through space in the form 
of individual photons — not unlike the 
Newtonian corpuscles — received such 
strong support that its validity could 
not be doubted 

3 35 One of the most significant 
arguments for the photon, or particle, 
nature of radiation is provided by the 
discovery of what is known as the 
Compton effect, made by the Amencan 
physicist A H Compton m 1923 He 
found that when X rays fall on carbon, 
or other material of low atomic iveight, 
the scattered radiation contains some 
ravs of longer wave length than the m- 
cident X-rays Since the scattenng is 
actually produced by the electrons 
present in the carbon atoms, it appears 
that interaction between X-rays and 
electrons results in an increase in the 


Aiomte Energy Chap IJl 

wave length of the former By assum- 
ing the X rays to consist of particles of 
fenergy hv, where v is the frequency of 
the incident rays, and supposing that 
the encounter betiveen one of these 
particles and an electron is just like a 
collision between two rigid spheres, 
Compton deduced equations which 
account perfectly both for the increase 
m wave length of the scattered X-rays 
and for the simultaneous recoil of the 
struck electron (Fig 3 5) 



Pia 3 5 The Compton effect accom- 
panying the mteraction of an X-ray photon 
with as electros 

3 36 Ionization by X-rays appar- 
ently requires a direct encounter be- 
tween an X-ray photon and an electron 
present m the atom or molecule to be 
ionized Since such encounters are not 
too common, it is possible to under- 
stand vhy the extent of ionization pro- 
duced by X rays is less than would be 
expected from a wave motion spread- 
ing in all directions 


WAVES AND PABTICLES 


Wave-Particle Duality 
3 37 The situation now reached ap- 
pears to be contradictory having firet 
established, fairly convmcingly, that 
radiations consist of electromagnetic 
waves, it has now been shown, equally 
convmcingly, that radiations arc emit- 


ted, transmitted through space, and 
absorbed as energy particles! How- 
ever, a more careful exammation of 
the state of affairs will show that there 
IS a possible way out of the apparent 
paradox The diffraction and interfer- 
ence properties of radiation necessitate 


• From the Greek photos meaning li^t The term photon which came into general use 
3und 1923 was introduced by A H Compton (see 5 3 35), following its earlier employment 
* • - ... ‘aby the noted Amencan physical chemist, 


around 1923 was introduced by A 1 . . 
in a somewhat different, but related, < 

G N Lewis 

Although the photon is frequently regarded as anonymous with the energy quantum it k 
strictly the quantity or quantum of radiation assoaated with a single quantum of energy It 
might in fact be described as an atom or particle ' of radiation By equation (3 2) a 
photon of radiation of frequency y camca an amount hy of energy 



69 


Energy and Radiation 


a wave structure, but photoelectric 
phenoniena and the Compton effect 
imply that radiation consists of parti- 
cles rather than waves. In other words, 
radiation may be regarded as having 
a dual w'ave-particle nature, some of 
the properties of radiation may be wave 
properties’, while others are particle 
properties. 

3.38. This dualism of the wave and 
particle functions of radiation led Loiiis 
de Broglie of France to suggest, in 
1923, that a similar dualism might 
exist for material particles and elec- 
trons. His proposal was, essentially, 
that the wave-particle dualism repre- 
sented something that is perhaps 
fundamental to the nature of the uni- 
verse. By means of Planck’s quantum 
theory equation and the mass-energy 
relationship of Einstein, to be consid- 
ered shoi’tly (§ 3.71), de Broglie showed 
that a particle of mass m moving with 
a velocity v should be associated with 
waves of length X, given by 

X = A, (3.6) 

mv 

where h is the Planck constant. Simi- 
larly, radiation of wave length X, will 
be equivalent to a particle of mass 
h/'Kv, moving with speed u, w^here in 
this case v is the velocity of light. 

3.39. XYithout going into details, it 
can be seen from equation (3.6) that 
the wave length is inversely related to 
the product of the mass and velocity 
of the particle; this product, i.e., mv, is 
knoTsm as the nioincntinn of the parti- 
cle. Actual calculations show that un- 
less the mass in is verj' small, such as 
would be the case for an electron or for 
the lightest known atoms, namely, 
hydrogen and helium, the wave length 
of the matter leaves, as they a.re often 
called, arc so short that there are no 
means at present available for their 


detection. Nevertheless, there is little 
doubt that something with a waveUke 
character is always associated with a 
moving particle, although it is different 
from the electromagnetic waves of light 
and other radiations. 

3.40. It was mentioned in § 2.88 
that crystals can act as diffraction grat- 
ings and can produce interference effects 
with X-rays, since the spacing of 
atoms and molecules in crystals are 
of the same order as the wave lengths 
of these rays. Soon after the publica- 
tion of de Broglie’s n'ork, the sugges- 
tion was made in 1925 by W. Elsasser, 
in Germany, that evidence for the 
wmve nature of electrons might be ob- 
tained in an analogous manner. From 
the known mass of the electron (§ 2.56), 
it was calculated that with a moder- 
ately high velocity, such as could be 
obtained by passage through a poten- 
tial of about 100 to 1000 volts, the de 
Broglie waves should have a wave 
length of the order of 10~® cm. If this 
were the case, then crystals should be 
capable of producing diffraction effects 
wdth electrons. 

The Diffraction op 
Electrons and Atoms 

3.41. The first definite proof that 
electrons can be diffracted and conse- 
quently exhibit wave, as well as the 
familiar particle, properties was ob- 
tained in the BeU Telephone Labora- 
tories in New York by C. J. Davisson 
and L. H. Gei-mer in 1927. By study- 
ing the reflection and scattering, by a 
nickel crystal, of a beam of electrons, 
given a specific velocity by passage 
tlirough a known potential difference, 
it was found that the electrons behaved 
like waves rather than as particles. 
TJsmg electrons which had been accel- 
erated by a potential of 54 volts, the 
e.xperimental results were found to be 
equivalent to those expected from ra- 



70 Sourcebook on 

diation of wave length 1 65 A This 
was in remarkably good agreement 
with the value of 1 67 calculated by 
means of the de Broghe equation (3 6) 

3 42 Further evidence for the exist- 
ence of electron waves was obtained 
independently in 1927, by the English 
physicist G P Thomson, son of J J 
Thomson He passed a stream of fast 
moving electrons through a very thin 
sheet of metal, and then allowed the 
resulting beam to fall on a photo- | 
graphic plate Upon development, the 
plate showed a diffraction pattern con- 
sisting of a series of concentric circles, 
just as might have been produced by 
X-rays, indicating that the electrons 
were manifesting wave properties It 
IS of special interest to mention that 
the diffraction pattern could be dis- 
torted by means of a magnet, showing 
It was actually produced by electrons 
and not by extraneous radiations, 
such as X-raya, which might have been 
present Since 1927, the wave proper- 
ties of electrons have become almost 
commonplace in scientific laboratones 
The electron microscope, for example, 
which IS used for the examination of 
particles much too small to be visible 
m the best optical instruments, de- 
pends on the behavior of electrons as 
waves although diffraction is not m- 
volved 

3 43 Diffraction effects have been 
observed with streams of hydre^en 
and helium atoms — actually ions, i e , 
protons and alpha particles, were used 
since they could be speeded up by 
means of an electric field — and even 
ivith neutrons It is thus apparent 
that these particles which are two 
thousand, and more, times as heavy 
as the electron, also have wave prop- 
erties There is little doubt that rf 
suitable detecting means could be 
devised, even heavier atoms and 


Aiomte Energy Chap HI 

molecules would be found to edubit 
the diffraction effects characteristic of 
wave motion At the present time, 
there does not appear to be any way 
m which this might be accomplished 
3 44 In view of the wave particle 
duality of matter, it may be wondered 
if there is any point in making a dis- 
tinction between a wave and a particle 
In a sense, such a distinction is mean- 
ingless, since everything has wave 
cbarecter or particle character depend- 
ing on the circumstances Neverthe- 
less, it IS still the general practice to 
refer to an electron, a neutron, an 
atom or a molecule as a particle, 
whereas light, gamma rays and X rays 
are regarded as waves This is done 
because the familiar properties of the 
former group correspond to those asso- 
ciated with particles, but the members 
of the latter group commonly behave 
as %vave5 A more satisfactory ap- 
proach would be to differentiate be- 
tween particle properties and wave 
properties, rather than between parti- 
cle and wave Electrons, atoms and 
BO on, usually exhibit particle proper- 
ties, whereas light, gamma rays and 
similar radiations, normally manifest 
wave properties But, if suitable con- 
ditions are established, the electrons 
and atoms will behave like waves, 
whereas the radiations can act like 
particles 

The Uncektaintt Principle 
3 46 It was realized by W Heisen- 
berg, who was later in charge of Ger- 
many’s unsuccessful effort to develop 
an atomic bomb, that the wave-parti- 
cle duality of matter was merely one 
aspect of a general law of nature On 
the basis of highly involved theoretical 
considerations, Heisenberg, m 1927, 
enunciated the uncertainly principle 
which represents a generalization of 



71 


Energy and Radiation 


the greatest significance. For the pres- 
ent purpose, this principle may be 
stated in the following simplified form: 
The simultaneous exact determination 
of position and momentum, or of any 
property related to momentum, such 
as velocity or energy, is impossible. 
That this is the case may be illustrated 
by reference to the electron. Its posi- 
tion might be found, in principle, by 
illuminating it ^vith radiations of very 
short wave length, e.g., gamma rays, 
for example, and then observing it in a 
suitable (imaginary) supermicroscope. 
However, in this process of determin- 
ing the position of the electron its mo- 
mentum will change, because of the 
recoil resulting from the Compton 
effect, i.e., from the interaction of the 
electron \vith a gamma-ray photon. 
Consequently, although the position 
of the electron might be obtained very 
exactly, the momentum could not 
possibly be estimated with any degree 
of accuracy. 

3.46. At first sight, it seems that 
this difficulty might be overcome by 
making use of the wave character of 
the electron and measuring its wave 
length, by means of an appropriate 
diffraction grating; the momentum 
could then be calculated exactlj'^ by 
means of the de Broglie equation (3.6). 
But this de\dce would be of no avail. 
Since the electron wave undergoes 
diffraction, in the determination of the 
momentum, its direction of motion is 
changed and the position of the elec- 
tron is no longer defiined. No matter 
what method is employed, the final 
result is inescapable: if the position of 
a particle can be determined exactly, 
then its momentum is indefinite, but 
if the momentum is obtained vnth. con- 
sidcmble precision, the position will be 
uncertain. In every case, there will be 
an inevitable interaction of the particle 


under observation with the measuring 
system, so that if either the position or 
the momentum is determined accu- 
rately, the other will be indefinite. It 
is important to emphasize that these 
circinnstances are not due to experi- 
mental errors, but to a fundamental 
characteristic of nature. 

3.47. It can be seen from the forego- 
ing discussion that when investigating 
the precise position of an electron, it 
is treated as a particle, but if its mo- 
mentum is required, then use is made 
of the wave properties. Similar con- 
siderations apply to all particles and 
also to radiation. This means that for 
certain purposes a system may be 
treated as a particle, and for other 
purposes as a wave motion, but it can- 
not be considered as having both par- 
ticle and wave characters simultane- 
ously. Thus the wave and particle 
properties of matter and radiation are 
to be regarded as complementary and 
not contradictory. 

Wave Mechanics 

3.48. In order to determine the fu- 
ture behavior of a moving particle by 
means of Newtonian or classical me- 
chanics, it is necessary to know both 
its position and momentum at any 
particular instant. According to the 
uncertainty principle, however, these 
two quantities cannot be precisely 
knowm at the same instant, and so the 
behavior of the particle cannot be pre- 
dicted. This statement would appear 
to be contrary to experience, since cal- 
culations relating to the motion of 
both terrestrial and celestial bodies 
have proved remarkably accurate. 
Tlie explanation is that for bodies of 
appreciable mass, the uncertainty in 
the determination of either the posi- 
tion or the momentum is so very small, 
both relatively and absolutely, that it 



72 


Sourcebook on Atomic Energy 


13 less than the normal experimental 
error of observation * The use of clas- 
sical mechanics in such cases gives re- 
sults winch are, at least, as accurate 
as the actual measurements 
3 49 When dealing mth very small 
particles, such as electrons and other 
constituents of atoms, however, the 
situation is verj different The uncer- 
tainties are here so relatively large 
that classical mechanics is virtually 
useless For the treatment of such 
minute particles a new procedure, 
knoum as quantum mechanics or wave 
mechanics, in which the apparent cer- 
tainties of classical mechames are re- 
placed by probabilities, ^\ os introduced 
by the Austnan-bom physicist E 
Sebrodmger in 1926 and developed by 
himself and by others t It is difficult 
to ascribe an exact physical significance 
to the mathematical treatment, but Jt 
may be thought of eomew hat along the | 
following lines The position of an 
electron, or other particle, of definite 
momentum or energy cannot be known 
exactly, because of the operation of the 
uncertainty principle, and it is possible 
to state only the statistical probability 
that the particle uill be found at any 
Riven point Since it has been estab- 
lished that particles can exhibit what 
appear to be wavelike properties, the 
new mechanics postulates that this 
probabibty can be expressed by means 
of a relationship which is similar to 
that used for describing wave motion 
in general The situation, as far as it 
can be given a physical interpretaticai, 

IS that the statistical probability of 
finding a particle m a particular place 
can be represented by an equation of 


Chap HI 

the same form as that which describes 
the propagation of waves 
3 BO It should be admitted quite 
frankly that at the present time the 
mathematical apphcations of wave 
mechanics have outrun their interpre- 
tation in terms of understandable re- 
alities There is little doubt, in view 
of their remarkable success in various 
atomic studies, that the equations of 
wave mechanics are substantially cor- 
rect, but their underlying sigmficance 
IS by no means obvious Some scien- 
tists are content with the mathematics 
alone, for they consider that its exact 
physical meamng is beyond human 
comprehension at present Louis de 
Broglie, for example, said "Recent 
theoretical views suggest that a mech- 
I anistic view of nature cannot be pushed 
i beyond a certain point, and that the 
fundamental laws can only be ex- 
pressed m abstract terms, defying all 
attempts at an mtcUigible desenp- 
tion ” Even among those who attempt 
an interpretation m material terms, 
there is no complete agreement At 
any rate, the point of view expressed 
in the preceding paragraph, which is 
based on that of Max Bom (1926), 
even if not absolutely true, does pro- 
vide a fairly simple, convenient, and 
probably not too misleading way of 
considering the postulates and results 
of wave mechames Some of these re- 
sults as applied to atomic properties 
ivill be considered in later chapters 

Significance of Wave 
Properties 

3 Bl. Although it is admitted that 
particles are associated with wavehke 


• According to the uncertainty principle the product of the uncertainties m the dete^na- 
tion of the position and momentum is appromnately equal to the Planck constant «, i e p 
6 62 X 10'*’ erg sec (or gram cm */seo ) Por a body of appreciable mass this unMrtainty 
effect IS negligible, but for an electron, with a mass of lO"** gram, or even for a light atom, 
such 13 evidently not the case „ . ^ v j a 

t Wave mechanics should really be used for aQ eystems, large or small But, for owies 
larger than a single molecule, the results are essentially identical with those derived from 
classical mechames, so that the latter, which is considerably simpler, is invariably employed 



73 


Energy and Radiation 

properties, the nature of the so-called space is still a myster}^ There is little 
matter waves of de Broglie still pre- doubt that this vieAv, like many other 
sents a problem. It is known that they scientihc theories, will have to undergo 
are not electromagnetic waves, like modification in the future, but for the 
X-rays or gamma rays, although they present it maj'' be accepted, at least as 
may have similar wave lengths, but a working hypothesis, 
what they are is not evident. If the 3.62. Similar considerations may 
interpretation of wave mechanics given conceivably apply to radiations. Al- 
above is accepted, a possible solution though these are still referred to as 
of this problem may be found, for the electromagnetic waves, for they are 
matter waves would not represent an undoubtedly associated with electric 
actual wave propagation. A stream of and magnetic fields which obey a wave 
moving particles behaves like a train of equation, there is not necessarily any 
waves merely because the statistical wave motion. It may perhaps be per- 
probability of finding a particle at any missible to consider I’adiation as con- 
point in its path is represented by a sisting of photons whose statistical dis- 
wave equation. ^^Tiy such an equation, tribution is represented by an equation 
rather than some other form, should of the form applicable to the propaga- 
give the distribution of the particles in tion of waves. 

RELATIVITY AND THE MASS-ENERGY EQUATION 

The Etheh and the was strengthened. In addition to carry- 

Velocity of Light ing radiation, it pro\dded the medium 

3.53. When physicists in the early propagation of electromagnetic 

years of the nineteenth century were disturbances. No one could say ex- 
developing the wave theory of light, ^ictly what the ether was, and there 
they considered the waves to have re- proof of its existence; nev- 

ality and so it was felt there should be ertheless, the view w^as widely ac- 
a medium which carried them. Just as cepted that the ether had real sigmfi- 
ripples on the surface of a pool are 

transmitted by the water, and sound 3.64. Various astronomical measure- 
requires air or other material, so it ments had led to the conclusion that 
seemed that a medium was necessarj’^ ether, if it exists, is stationary, and 
for the jiropagation of light waves. It that bodies such as the earth, sun and 
was postulated, therefore, that there through it without produc- 

cxisted an all-pervading Imniniferous any disturbance. If this were the 
(or light-hearing) ether, a view which, case, then it should be possible to de- 
incidentally, is no longer accepted, termine the absolute speed with which 
Since light ivaehes the earth from dis- earth is moving through space bj^^ 
t ant stars in outer space, the ether was obsen'ations on the velocity of light, 
presumed to extend indefinitelj’-, so Suppose the earth travels through the 
that it was regarded as virtually iden- stationary ether at an absolute speed 
ticid with space itself. Mien Maxwell of a, say in miles per hour. Consider a 
.‘-'howTd that light was associated with fixed source on the earth from w'hicli 
a vai^-iug electromagnetic field (§3.23), light is emitted; let c be the speed of 
the liehet m the hj-pothetical ether light througli the ether. If the direc- 



74 


Sourcebook on Afomtc Energy 


tion of propagation of light happens to 
coincide wth that in which the earth 
IS moving, the velocity of the light rel- 
ative to the ether will be c + *» If, 
however, the light travels m the direc- 
tion exactly opposite to that of the 
earth, itsrelative velocity iviH bee — v 
The situation is similar to that of a 
man swimming with a speed o in a 
nver fiowmg at the rate v, if the swim- 
mer travels in the direction m which 
the nver is flowing, his speed relative 
to a pomt on the nver bank will be 
c -h v But if he travels in the opposite 
direction, his speed wiU be c ~ w 
3 65 ilie time taken for the hght to 
travel a defimte distance I in the direc- 
tion of the earth’s motion is then 
l/(e 4- v), while the same distance in 
opposite direction will require the 
time l/{c ~ v) Hence, if light were to 
travel a certain distance I m the direc- 


Chap 2J2 

perpendicular to the earth’s motion 
The speed will be unaffected by the 
movement of the earth, and the light 
inll travel to and be reflected from a 
certain point with the velocity c, its 
absolute speed through the ether 
However, because of the supposed 
motion of the earth through the ether, 
Ae distance over which the hght has 
to travd will be increased This case is 
exactly analogous to a man swimming 
in a direction perpendicular to that of 
the nver’s flow His actual path will be 
as represented by the broken line m 
Fig 3 6, rather than by the full hne, as 
would have been the case if the river 
had been stationary It is a simple 
matter of geomet ry to s how that the 
path is now fc/V ^ — e*, instead of I 
Hence the time taken for the li^t to 
travel , at the speed c, in each direction 
13 f/Vc* — V*, so that 


Time for travel peipendicular to earth’s motjoa 

- ■ j-- r ^ - 2f_ 

Vc* - Vc* — V* Vc* — V* 


tion m which the earth is moving, then 
be reflected back and travel the same 
distance m the opposite direction, the 
time required would be given by 


The ratio of the tunes for propagation 
of hght parallel and perpendicular to 
the earth's motion is then obtained by 
dividing the two expressions, thus, 


Tvma icx naraJlRl bi eaxtb.’a wMjjwl — — \ b — ^ 

^ C’hvC'-vc- — ir 


3 66 Suppose now that the light 
coming from the source on the earth is 
propagated in the ether m a direction 



Ratio of times = 


2cl 

c* - D* 



1 

Vl - 


(3 7) 


3 67. The speed c at tvhich light 
travels is known, namely, 186,264 
miles, or 2 99776 X cm , per sec , 
hence, if the ratio of the tunes required 
for the light to travel m the two paths 
at right angles could be measured, the 


Fio 3 6 Path of swimmer crossmg 
stream at right angles to direction of 
flow 



75 


Energy and Radiation 


value ot V, the rate at which the earth 
nioves through the ether, could be 
readily calculated from equation (3.7). 

The Michelson-Mohley 
Experiment 

3.68, If a means could be devised for 
dividing a beam of light from a given 
source into two rays propagated at 
right angles to one another, making 
them travel the same distance to a 
mirror where each is reflected back, 
and comparing the times of arrival of 
the two rays, the problem of deter- 
mining the earth’s speed through the 
ether would, presumably, be solved. 
The first reliable measurements of this 
kind were made in Potsdam, Germany, 
by the noted American physicist A. A. 
Michelson in 1881. The results were so 
unexpected that the work was repeated 
by Michelson, in Cleveland, Ohio, in 
conjunction with E. W. Morley. In 
1887, a report of the historic Michelson- 
Morley experiment was published: it 
was found that there was no signifi- 
cant difference between the rates at 
which the light traveled in the two di- 
rections at right angles to each other. 
Various orientations of the beams were 
tried, but the results were always the 
same; the speed of light was independ- 
ent of its direction of propagation.* 
3.69. The Michelson-Morley experi- 
ment thus showed that the ratio of the 
times of travel of light in equation (3.7) 
is virtual^ unity, and this presumably 
meant that i>, the rate at which the 
earth moves tlirough the ether, is zero. 
In other words, it appeared that the 
earth docs not travel through a star- 
tionoT}' ether, but carries the ether 
along until it. Tliis surprising conclu- 
sion represented a complete contradic- 


tion of the long accepted view that the 
earth, and other bodies, moved through 
the ether udthout disturbing it, and 
consequently it created a sensation in 
the world of science. 

3.60. In seeking for a way out of the 
dilemma, the Irish scientist G. F. Fitz- 
gerald (1893), while retaining the sta- 
tionary ether hypothesis, suggested 
that a body traveling in a direction 
parallel to the earth’s motion actually 
undergoes a contraction. This contrac- 
tion would not normally be observed 
because the measuring instrument 
would contract correspondingly, and 
the distance would appear to be un- 
changed. Thus, it was supposed that 
in the Michelson-Morley experiment 
the apparatus changed its dimensions 
in such a Avay as to compensate exactly 
for the expected difference in the veloc- 
ity of light in the two directions at 
right angles. The ratio of the velocities 
would thus appear to be imity. Ac- 
cording to Fitzgerald, the contraction 
in the direction of the earth's motion 
w ould be represented by the factor 
Vi — dVc^j which is, of course, identi- 
cal with the denominator of equation 
(3.7). 

Velocity and Mass 
OP THE Electron 

3.61. It was indicated in § 2.57 that 
the mass of an electron varies with its 
speed. The first evidence of such a 
variation was obtained by W. Kauf- 
mann, who had made some of the very 
earliest measurements of the specific 
charge of an electron (§ 2.43). In 1900, 
he described a method for determining 
c/m for high-velocity beta particles 
from a radioactive source, making use 
of deflections in electric and magnetic 


a quarter of that expected for a stationary ether, was ol 
'fisregarded. However, os a result of numerous observations made h 
Morley with D. C. Miller (1M2-1905) and’ by ^filler alone (1921-m2), StteTcSude 

bas real significance. Newrthcless, other experimenters consider that tt 
dL^crepancy is due, mainly if not entirely, to c.xperimental errorV ^vnamer mat tr 



76 


Chap in 


Sourc^xx^ on Aiorme Energy 


fields The experimental arrangement 
was such that differences m the veloci- 
ties of the beta-ray electrons could be 
detected at the same time, and it ap- 
peared that the ejm value decreased 
slightly as the velocity increased This 
conclusion was apparently confirmed 
byA H Buchererin 190S,*andbyE 
Hupka in 1910, the former used beta 
rays, and the latter highly accelerated 
cathode rays, as the source of electrons 
Provided the speed of the electrons is 
less than about one tenth of the veloc- 
ity of light, the specific charge c/m is 
essentially constant, but as the speed 
increases, the values of ejm exhibit a 
definite decrease If, as is very prob- 
able, the actual charge c of the electron 
IS independent of its velocity, it must 
be concluded that the mass of an elec- 
tron increases as its speed is increased 
3 62. In the course of his studies m 
mathematical physics, the great Dutch 
scientist H A Lorentz had derived an 
expression relating the mass of an elec- 
tron to Its speed His arguments may 
be stated in the following elementary 
form A movmg electron is assumed to 
contract in the direction of its mot ion 
by the Fitzgerald factor Vi — v*/c*, so 
that if To 13 its rad ius when a t rest, the 
value vull be roVl — v^/(? when the 
electron is moving with a speed v If 
the mass of a spherical electron is as- 
sumed to be electromagnetic m nature, 
then by equation (2 11) the mass 
should be mversely proportional to the 
radius Representing the rest mass of 
the electron, i e , the mass for very 
small velocities, by nuj, and its mass 
when moving with the speed v by the 
letter m, it consequently follows that 

m _ro 1 

wa ” ro (Vl - v‘/<?) Vl - i»Vc* 



3 63, Since the factor Vl — i)2/c* is 
always less than unity, it is seen that 
the mass m of the electron when mov- 
ing with a speed v should be greater 
than the rest mass wio If t> is about one 
tenth of th e velocity of hght, i e , v/c is 
0 1, then Vl — v^/<? is 0 995, and the 
actual mass w is 1 005 mo, differmg 
from the rest mass by only 0 5 per cent 
But, if V IS 99 per cent of the speed of 
li^t, so that v/c is 0 99, then the actual 
ma^ will be 7 10 times the rest mass 



y/t 


Fig 3 7 Increase of mass, relative to 
its rest mass, of a moving particle with 
mcreasmg velocity. 

As the speed of the electron approaches 
that of light the ratio m/mo should in- 
crease very rapidly, as shown in Fig 
3 7 The expenmental determination 
of e/m for electrons moving at various 
speeds up to about eight-tenths of the 
velocity of light, are m excellent agree- 
ment ivith equation (3 8), so that this 
may be taken as giving a satisfactory 
representation of the effect of motion 
on the mass of an electron 


• More recent work has shown that Budierer’a expenmental procedure was not capable of 
giving the degree of accuracy which be claimed for ms results 


Energy and Radiation 


77 


The Theory of Eelattvity j 

3.64. The Lorentz equatioa for the 
influence of speed on electron mass is 
undoubtedly of the correct form, but 
the arguments upon which it was based 
have proved inadequate. However, in 
1905, using his theory of relativity, the 
German-bom Albert Einstein, at the 
time an examiner in the Sndss Patent 
Office, derived an expression identical 
with equation (3.8), but applicable to 
all moving particles, and not merely to 
electrons. The important point is that 
for all bodies, whether they carry an 
electric charge or not, and regardless 
of whether their mass is electromag- 
netic in origin or not, the mass should 
increase with increasing velocity. The 
reason why such an increase of mass is 
not usually observed will be clear from 
Fig. 3.7 ; it -will not be detectable until 
the speed approaches that of light, for 
it is only then that 7n/m<^ becomes ap- 
preciably gi'eater than unity. Such 
high speeds are, of course, unusual. 
They can be obtained with beta parti- 
cles from radioactive sources, and with 
specially accelerated electrons and 
other charged particles (Chapter IX) ; 
in these cases, there is no doubt that 
the mass does increase with the speed. 

3.66. In attempting to explain the 
Michelson-Morlej’’ experiment, Ein- 
stein first discarded the ether concept 
as unnecessary; he then made two as- 
sumptions: first, that determination of 
absolute motion is impossible, and, 
second, that the velocity of light alwmys 
luTs a constant value, irrespective of 
the motion of the source or of the ob- 
seiv'er. These two postulates formed 
the basis of the special ihcorij of relativ- 
ity, which Einstein used to obtain re- 
sults that h.ave had a profound effect 
on many brandies of science. It is not 
possible here to do more than touch 
verj* .superficially on such aspects of 


the theory as are applicable to the 
problem of atomic energy. 

3.66. Suppose a signal lamp flashes 
a beam of light of velocity c down a 
railroad track, along which a train is 
traveling at a speed v; according to the 
larvs of classical mechanics, to an ob- 
server on the train, the speed of light 
relative to himself should be c -|- w if he 
is moving toward the signal, or c — a if 
he is traveling away from it. But the 
theory of relativity, based on the re- 
sults of the Michelson-Morley experi- 
ment, states that the observer on the 
train will always find the velocity of 
light to have the constant value c, rela- 
tive to himself, no matter in what di- 
rection he is moving. The explanation 
is that, although the observer does not 
realize it, his instruments for measur- 
ing both distance and time, which are 
necessary for determining velocity, are 
imdergoing change as the train moves 
in one direction or the other. As a re- 
sult of these changes the observer ■will 
always find the velocity of light to have 
the same value regardless of the direc- 
tion of his motion. Another observer 
who remains stationary -with respect to 
the signal lamp would, in theorjq be 
able to detect the changes in the meas- 
uring instruments on the moving train, 
\vith respect to his o-um stationary in- 
struments. 

3.67. In order to satisfy the require- 
ments of the theory of relativity, meas- 
urements of length and time made "with 
respect to a mo%dng body have to be 
converted, by the use of certain mathe- 
matical transformations, to give the 
corresponding values with respect to 
a stationar}’' body. Thus, length and 
time are relative, and not absolute, 
quantities, the values depending on the 
motion of the body -uith respect to 
which they are measured. 

3.68. These relat ivity corre ctions in- 
volve the term VT- encoun- 



78 


Sourcebook on Atomic Energy 


tered m the preceding paragraphs, 
which does not differ appreciably from 
umty until the velocity v of the moving 
body is as high as about one tenth of 
the speed of light Hence, for speeds 
which are small relative to the velocity 
of light, e g , up to about 18,000 miles 
per second, but nevertheless, extremely 
high by ordinary standards, the cor- 
rections are quite negligible Under 
normal conditions, therefore, it would 
not be possible to detect the expected 
changes m the instruments for deter- 
mining length and time, classical me- 
chanics IS then adequate for treating 
moving bodies From what has been 
stated here and in § 3 48, it is evident 
that Newton’s laws of motion represent 
what are called limiting laws Although 
they are entirely adequate for the limit- 
ing cases of relatively large bodies, i e , 
larger than a molecule, moving with 
moderate speeds compared with that of 
light, they break doivn when applied to 
particles of small dimensions traveling 
with very high speeds It is these latter 
conditions which exist w ithin the atom , 
consequently, in atomic studies new 
laws based on wave mechanics and 
relativity must replace the classical 
laws of motion 

The Mass-Enerot Relationship 
3 69 In the further development of 
his theory, Einstein was able to show 
that similar considerations apply to 
mass as to length and time, the trans- 
formation factor required to convert 
the mass of a moving body to the rest 
mass was found to be identical rsoth 
that derived by Lorentz for the elec- 
tron, so that equation (3 8) given above 
holds for any system It is often re- 
ferred to as the relctimtic mass egua- 
tion, the mass m being called the rela- 


Chap in 
iwtshc mass, to distinguish it from mo 
the rest mass, for low velocities 
3 70 Writing equation (3 8) m the 
equivalent form 

m « mo (1 - uVe*)"’", (3 9) 

and expanding the right hand member 
by means of the ell-known binomial 
theorem of algebra, all terms beyond 
the first being neglected since they are 
usually very small, the result is 

„ = + (310) 

The quantity Hwov* is approximately 
the kinetic energy of the body due to 
its motion wth a speed v (| 3 5), rep- 
resenting this by Ek, equation (3 10) 
may be written as 

m e mo -f- 

or, 

m — mo “ 

where, as usual, c is the velocity of 
li^t The quantity m — m©, the dif- 
ference between the mass of the mov- 
ing body and its rest mass, may be 
represented by Am, so that 

Am = # (3 11) 


The increase m mass Am of a body as a 
result of its motion is thus directly re- 
lated to the kinetic energy Ek Hence, 
it would appear from the theory of rel- 
ativity that there is a definite mass 
equivalent of energy, at least of kmetic 
energy ^ 


• The denvation of equation (3 11) given here is simple but very approxuuate A more 
exact procedure, using c^oulus is the foUowiog A force F acting on a body moving 
a distance dx increases the kmetic energy by Fdx, which may be represented by dA ny 
Newton 8 second law, force is equal to the rate of change of momentum bo that r * a[Tnv)/at, 



79 


Energy and Radiation- 


3.71. By the use of more detailed j 
calculations, Einstein proved, as he put 
it, that "the mass of a body is a meas- 
ure of its energy content” and that 
when the energy of a body is changed 
by an amount E— no matter what 
form the energy takes — the mass of 
the body will change in the same sense 
by E/(?. Consequently, it is possible 
to write the general relationship 

E = me, (3.12) 

wlierc the mass m is the equivalent of 
the energy E. This result, often re- 
fernd to as the Einstein mass-energy 
equation, is fundamental to the whole 
subject of atomic energy. It shows that 
there is an exact equivalence between 
energy and mass, and it points to the 
possibility of releasing large amounts 
of energy by the "destruction” or, 
more exactly, by the conversion, of 
mass. 

The CoNSEnvATiON of 
Mass and Energy 

3.72. In the early years of the pres- 
ent centurj'', there were two scientific 
laws which -would liave been univer- 
sally regarded as completely inviolate. 
They were the laws of the conse^^mtion 
of mass and of the consen^ation of en- 
ergj", which stated that matter, deter- 
mined as mass, and energj’^ can neither 
be crcjited nor destroyed. From the 
time of the Greek philosopher Anaxa- 
goras, about 450 B.C., through that of 
Francis Bacon, who in his Novum Or- 
gamim, published in 1620, vTote: 
". . . the absolute quantity or sum 
total of matter remains unchanged 
without inciease or diminution,” and 
of A. L. Lavoisier in the latter part of 


the eighteenth century, up to recent 
years, the indestructibility of matter 
(or mass) had been regarded as axio- 
matic. In fact all the quantitative 
aspects of chemistry involved the tacit 
assumption that there was no net 
change of mass in a chemical reaction. 
The extremely accurate and painstak- 
ing experiments of H. Landolt (1909) 
in Germany and of J. J. Manley (1912) 
in England showed that if there was 
such a gain or loss of mass, it could not 
exceed about one part in a hundred 
million, this being the limit of accuracy 
of the balances used for w^eighing. 

3.73. The nature of heat and its rela- 
tionship to energy was only vaguely 
understood until the end of the eight- 
eenth century when, in 1798, the 
American-bom Benjamin Thompson, 
Count Rumford of the Holy Roman 
Empire, and Minister of War in Ba- 
varia, published a paper entitled An 
Enquiry Concerning the Source of Heat 
which is Excited by Friction. From 
studies made in the boring of brass 
cannon, he showed there is a direct 
connection between the heat generated 
and the mechanical work done. From 
the subsequent investigations of the 
English scientist Humphry Da-vy 
(1812), of the German physician J. R. 
Ma3’^er (1842), of the Danish philoso- 
pher L. A. Golding (1843) and of the 
English brewer turned scientist J. P. 
Joule (1843-1878), the exact equiva-. 
lence between work and energy was 
definitelj’’ established. 

3.74. The fundamental implications 
of these studies was realized by the 
famous German phj'^sicist H. von 
Helmholtz, who in 1847 enunciated the 
concept of the consenmtion of energy. 
The essence of this principle is that al- 


and consequently dE Fdx = (i(mc)dx/d(. Since dx/dt represents the %’-elocitv of the mov- 
frtS V tepbeed by v; consequently dB = rd(mv), or dE = t^dm~-j- vivdv. Dif- 

fea-nlmtion of the rclatm.^lic mass equation (3.S), in the form m* (c= - e*) = WoV, rives 

f ‘’■''ir 7 ^ constant. Comparison with the precedinir eaua- 

ttnn for dh shows that dm = rfEM which is similar to, but more exact than, equation (3. U). 



80 


Sourcdtotw on Aiomtc Energy Chap III 


though one fonn of energy may be con- 
verted into another form, it can neiUier 
be created nor destroyed In other 
words, whenever there is a production 
of energy of any kind, such as work, 
heat or electncal energy, an exactly 
equivalent amount of another kind 
must ha.^ e been used up Support for 
this law was provided not only by fail- 
ure of the innumerable attempts to 
achieve perpetual motion, i e , the con- 
tmuous production of mechanical en- 
ergy without the use of a correspondmg 
quantity of some other form of energy, 
but, more significantly, by its un- 
doubted success m thermodynamics 
and engineering 

3 76 It would appear from the fore- 
gomg review that Emstein’s concept of 
the equivalence of mass and energy is 
entirely contraiy to the laws of conser- 
vation of mass and energy If a fast- 
moving body IS slowed down, its mass 
diould decrease, accordmg to the mass- 
energy relationship, if its motion is 
accelerated the mass should increase 
Similarly, if the mass of a system could 
be changed m any way, as is m fact 
possible for many processes taking 
place within the intenor of atoms, 
there should be a corresponding libera- | 
tion or absorption of energy Althou^ 
these conclusions are, at first sight, 
irreconcilable with the conservation 
laira, the fact is that both views are 
correct, provided they are properly 
interpreted 

3 76 Suppose a system undergoes a 
process of some kind, as a result of 
which it releases energy E, then, by 
the Einstein mass-energy equation, its 
mass will decrease by an amount E/t? 
But, it must be remembered, that the 
enei^ released will pass to another 
system or systems, whose mass will 
correspondmgly be increased by ex- 
actly E/c* The total mass of all the 
bodies concerned ivill consequently re- 


mam imchanged The conventional 
law of conservation of mass was re- 
garded, erroneously, as applying to the 
reactmg system only, but it is now seen 
that it must be extended to include the 
system, or systems, to or from which 
energy is transferred Further, if, as 
Emstem implied, the eneigy content of 
a body is related to its mass, by equa 
tion (3 12), it IS evident that smee 
there is no net gam or loss of mass, 
there will be no change m the energy, 
provided all the systems involved m a 
given process are included 
3 77 In view of the postulated 
equivalence of mass and energy, it may 
well be asked Why had changes in 
mass not been detected, especially m 
chemical reactions m which large 
amounts of energy are liberated as 
heat? This question can be readily an- 
swered by means of a quotation from 
the Principles of Science, by the Eng 
lish philosopher W S Jevons, pub- 
lished as long ago as 1879 "Physicists 
[and chemists] often assume quanti- 
ties to be equal provided they fall 
within the limits of probable error of 
the process employed . We cannot 
prove the mdestructibility of matter, 
for were an exceedingly minute fraction 
of existmg matter to vanish m any ex- 
periment we should never detect 
the loss ” In other words, a change m 
mass could not be detected if it were 
less than the experimental error, as it 
IS indeed m chemical reactions even 
where measurements have been made 
wiUi Uie greatest possible precision It 
is not surprising, therefore, that no 
evidence for the interchangeability of 
mass and energy has been obtained 
from a study of chemical processes 
When it comes to rearrangement 
within the atoms themselves, however, 
tire energy changes are very large in- 
d^d, and the corresponding changes of 
mass have been found to be m accord 



Energy and Radiation 


81 


with the Einstein mass-energy equa- 
tion. 

iNTEnCONVEUSION OF MaSS 

AJ>JD Energy 

3.78. A more detailed application of 
the mass-energy relationship to the 
subject of atomic energj’- wall be given 
in Chapter XI, and various references 
to it will be made elsewhere. At this 
point, it will be sufficient to illustrate, 
by means of a few' examples, the method 
of calculation and the general nature of 
the re.sults obtained using the equation 
E — TTK?, where E represents the energy 
equivalent of a mass m, and c is the 
velocity of light. If c is expressed in 
centimeters per second, and m in grams, 
then E will be given in ergs (§ 3.32 
footnote). Since the velocity of light is 
known to be 2.998 X lO*® cm. per sec., 
the Einstein mass-energy equation can 
be written iis 


E in the left-hand member, it follows 
that 

10<^ = X 2.15 X 10”, 
m = 4.65 X 10~® gram. 

The loss of mass equivalent to the en- 
ergy evolved w'ill thus be 4.65 X 10"® 
parts by weight in a hundred, W'hich is 
less than one in a billion. Such a de- 
crease is beyond the possibility of 
detection by even the most sensitive 
chemical balances. This is the reason, 
as indicated above, why the mass-en- 
ergy effect has not yet been observed 
in chemical reactions. 

Positron-Electron Pair 
Formation and Annihilation 

3.80. It w'as stated in § 2.77 that 
w'hen a positron and an electron anni- 
hilate one another, energy is produced 
W’hich appears in the form of gamma 


E ffirgs) = ni (grams) X (2.998 X 10“)® 
= m (grams) X 8.99 X 10®®. 

In raan 5 ' measurements, particularly 
where there is an evolution or absorp- 
tion of heat, as in chemical reactions, 
the energj' is expressed in heat units or 
calorics, 1 calorie being equivalent to 
4.184 X 10® ergs. Making this substi- 
tution, it is rcadily found that equation 

(3.13) takes the form 

E (calories) = in (grams) X 2.15 X 10 


(3.13) 

radiation. The magnitude of the en- 
ergj’ can be calculated from the mass- 
energy expression, and the frequency, 
or w'ave length, of the gamma ray can 
then be derived by means of the quan- 
tum theory. As seen in § 2.57, the rest 
mass of the electron is close to 9.11 X 
10"®® gi'am, and the positron presum- 

(3.14) 


3.79. Consider a process, such as the 
combustion of a hydrocarbon fuel, in 
w'lurh 100 grams of a chemical sub- 
stance undergo reaction with the liber- 
ation of 1 million, i.o., 10®, calories; this 
would mean the evolution of an excep- 
tiomally large amount of heat. Bj' 
means of equation (3.14) it is possible 
to calculate the decrease of mass to be 
exiwcterl. Substituting 10® calories for 


ablj' has the same mass; consequently, 
positron-electron anniliilation results 
in a loss of mass of 2 X 9.11 X 10"®® 
gram. Using equation (3.13), the ae- 
companjing liberation of energy should 
be 

E = 2 X 9.11 X 10-« X8.99 X 10®® 
= 1.64 X 10"® erg. 



82 


Sourcebook o 


3 81 In atomic studies it has be- 
come the practice to express energies m 
electron volt units, abbreviated to ev, 
rather than in ergs The electron volt 
IS the energy acquired by any charged 
particle carrying a unit (electronic) 
charge when it falls through a poten- 
tial of 1 volt, it IS equivalent to 1 603 
X 10"^* erg, but for present purposes 
It is sufficiently accurate to abbreviate 
this figure to 1 60 X 10"“ erg For con- 
venience, two other energy umts are 
used, one, equal to a thousand electron 
volts, called the kilo-electron volt, is rep- 
resented by Kev, and the other, which is 
a miUion electron volts, is abbreviated 
to Mev These are 1 60 X 10"® and 
1 60 X 10"* erg, respectively Hence, 
utilizing equation (3 13), the general 
mass-energy relation becomes 


Atomic Energy Chap III 

r,/,, V 6 62 X 10"” 
160X10- - 
= 4 13 X 10"*V per sec 

( 318 ) 

and 


E (Mev) 


1 99 X 10-» 


1 60 X 10-^ X cm 
^ 1 24 X 10~“ 

X cm 

From the latter, it follows that 
1 24 X 10-“ 


X (cm ) » • 


E (Mev) 


(319) 


(3 20) 


which IS a general expression relating 
the energy quantum (m Mev) to the 
wave length (m cm ) of the correspond- 
ing radiation 


Em (grams) 

-= m (grams) X 5 61 X 10” (3 16) 

E (Kev) = m (grams) X 5 61 X 10” (3 16) 

E (Mev) *s m (grams) X 5 61 X 10“ (3 17) 


Inserting the value of 2 X 9 11 X 
10"** gram, for the mass of a positron- 
electron pair, m equation (3 17) it is 
found that 

F = 2 X 9 11 X lO-** X 5 61 X 10“ 
= 1 02 Mev 

Hence the total energy accompanying 
positron-electron annihilation is 1 02 
million electron volts 

3 82 If the energy is hberated as 
one quantum of radiation, the fre- 
quency and wave length can be calcu- 
lated from the quantum theory equa^ 
tions (3 4) and (3 5) Dividing throu^ 
by 1 60 X 10** m each case, so as to 
convert ergs to Mev, these become re- 
spectively, 


3 83 Since E for positron-electron 
annihilation is 1 02 Mev, it is seen from 
equation (3 20) that 


1 24 X 10~“ 
102 


= 121 X 10-“cfo, 


which 13 0 0121 X 10- cm or 0 0121 k 
The corresponding frequency, which is 
rarely used, could be obtained from 
equation (3 18), if required 
3 84 It was assumed above that 
just one quantum of radiation is formed 
in positron electron annihilation It is 
more probable, however, that two 
equal quanta will be expelled in oppo- 
site directions, in order to conserve 
momentum, as required by the laws of 
mechamcs The energy of each quan- 



83 


Energy and Radiation 


turn will then be H X 1.02 Mev, i.e., 
0.51 Mev, and the wave length of the 
corresponding annihilation radiation 
will be 0.0242 A. The fact that radia- 
tions with wave lengths of about 0.012 
A and 0.024 A have been observed to 
accompany the disappearance of posi- 
trons is striking evidence for the con- 
cept of the equivalence of mass and 
energy, and for the applicability of the 
Einstein mass-energy equation in this 
case. 

3.86. Tlie mass equivalent of the 
photon of wave length 0.0242 A, i.e., 
2.42 X 10~'° cm., treated as a particle 
moving with the speed of light, can be 
calculated from the de Broglie equa- 
tion (3.6),* in the form vi = }i/\v, 
where h is 6.62 X 10“^ erg sec., X is 
2.42 X lO-^® cm., and c is the velocity 
of light, 3.00 X 10~*° cm. per sec. The 
result is found to be 9.11 X 10~^®gi’am, 
which is the same as that of the elec- 
tron (or positron). Hence, when a posi- 
tron and an electron annihilate one 
another, the photons produced have 
the same effective mass, so that mass, 
in the broadest sense, is conserved 
(§3.76). 

3.86. A further matter connected 


energy exactly equivalent to that lib- 
erated upon their annihilation, i.e., 
1.02 Mev. Hence, in pair formation by 
the thorium G" gamma rays, 2.62 — 
1.02 s= 1.60 Mev of energy should be 
left over which might be transferred to 
either the electron or the positron, or 
shared by both. In complete agree- 
ment with tliis expectation, experi- 
ments show that the maximum energy 
carried by a positron formed in this 
manner is 1.6 Mev. 

Mass-Energy Conversion 
Factors 

3.87. In many mass-energy calcula- 
tions It Is fovind oonvenlont to express 
masses on the atomic weight scale,'i.e., 
relative to the oxygen atom as 16.000. t 
As seen in § 1.64, the actual mass in 
grams of an atom or molecule is ob- 
tained upon dividing the atomic or 
molecular weight by the Avogadro 
number, 6.023 X 10“. Hence unit 
mass on the atomic weight scale! 
equivalent to an actual mass of 
1/(6.023 X 10“), i.e., 1.66 X 10-« 
gi’am. Upon inserting this factor into 
equations (3.13) and (3.17), respec- 
tively, the results are 


E (ergs) = in (at. wt.) X 1.49 X 10~^ (3.21) 

and 

E (jMev) = m (at. nd.) X 931, (3.22) 


with [)osii,ron formation is worthy of 
mention. It was slated in § 2.75 that 
gamma rays from thorium C" are able 
to produce po-sitron-electron pairs; the 
energy of these rays is kno\vn to be 2.62 
Mev. The creation of a positron-elec- 
tron pair will require an amount of 


where m (at. wt.) represents the mass 
on the atomic weight scale. It is seen, 
therefore, that 1 atomic weight unit is 
equivalent to 1.49 X IQ-^ erg or to 931 
Mev. By taking reciprocals of these 
.numbei-s, it is readily found that 1 erg 
is equivalent to 671 atomic weight (or 


wrallwl ihfti th(> dc Broplio equation acloally involves a combination of Planck’.s 
quantum oquatum and F.inslem s ma-ss-cnerpT.' relationship. 

chemical, atomic wciglit scale (§ 8.39) is used, but the dif- 
for ca!cubtion-s involving four significant figures or less 
owin sixteenth part of the mass of an 



86 


Source6oofc on Atomic 'Energy Chap 7F 

atom, it would mean that a sin^e an arrangement of positive and negar 
atom, especially of the heavier ele- tive electnc charges 
ments, would contam many thousand 

electrons However, m 1906, from con- Other Early T^ieories 

siderations based on the dispersion of 4 6 Two other view's on atomic 
light, and the scattenng and absorption structure which are worthy of mention 
of X-rays by gases, J J Thomson were proposed m the early years of the 
found that “the number of corpuscles present century One, by the Hungar- 
is not greatly different from the atomic lan, P Lenard (1903), was based on 
weight” This would mean that the his observation that swift cathode rays 
negative corpuscles, that is, the elec- could penetrate sheets of aluminum 
trons, contnbute only a very small and other metals (§ 2 19) It appeared, 
fraction of the mass of an atom, and therefore, that a large portion of the 
consequently “the mass of the earner atom consisted of empty space, and 
of unit positive charge is large com- Lenard suggested that the material 
pared with that of the earner of umt part was made up of neutral doublets, 
negative charge” These conclusions which he called “dynamids,” each con- 
were later proved to be substantially sistmg of a positive and a negative 
correct, but it was very difficult to reo- charge 

oncile them with the supposed nature 4 8 The second theory, published m 
of the positive charge distnbution 1904 by the Japanese physicist H Na- 
4 4 It must be admitted that scicn- gaoka, bears a stnkmg similarity to 
tists m general, and chemists in partic* the modem views on atomic structure 
ular, were not enthusiastic about these Its author compared the atom to the 
ideas on the nature of the atom, and planet Saturn, where stability is main- 
Lord Raylei^, m his biography of tamed by the attraction of the heavy 
J J Thomson, indicates that Thomson central body for the lighter particles m 
himself was not too He!! satisfied wth the surrounding nngs He then said 
them Nevertheless, some of his sug- “The present case [i e , the atom] wll 
gestions, particularly the one concern- evidently be approximately realized if 
mg the relationship between the change we replace these satelhtes by negative 
in properties of the elements in the pe- electrons and the attracting centre by 
riodic table and the groups of electrons, a positively charged particle” Naga- 
are not fundamentally different from oka used his picture of the atom to 
those now accepted Above all, Thom- make some calculations relating to the 
son’s theory was important because it spectra of the elements, but neither his 
called attention to the universality of speculations nor those of Lenard at- 
the electron, and indicated the possi- tracted any particular interest at the 
bihty that the atom might consist of time 

THE NUCLEAR ATOM 

The Scattering of by radioactive bodies (see Chapter II) 

Alpha Particles In 1906, Ernest Rutherford (§ 2 64), at 

4 7 The modern ideas concerning that time in Canada, had noticed that 
the structure of the atom arose directiy when alpha particles from a radioactive 
from a study of the radiations emitted source fall on a photographic plate, 



The Structure of the Atom 


87 


after penetrating a thin sheet of metal, 
the resulting trace is diffuse, fading off 
at the edges, instead of being sharp. 
This diffuseness was attributed to scat- 
tering of the alpha particles; that is to 
say, the particles were deflected from 
their course, presumably as a result of 
interaction with the atoms of the ma- 
terial through which they had passed. 

4.8. Two years later, when Ruther- 
ford was in Manchester, England, he 
was oxpeiimenting with alpha particles 
in collaboration with his German as- 
sistant Hans Geiger, who later achieved 
uno.xpected fame as the inventor of 
the Geiger tube (§ 6.25), and his at- 
tention was once again drawm to the 
scattering phenomenon. In the words 
of Geiger: “In the course of experi- 
ments undertaken by Professor Ruth- 
erford and m 3 ’-self to determine accu- 
rately the number of alpha particles 
expelled from 1 gi-amme of radium, our 
attention was directed to a notable 
scattering of alpha particles in passing 
through matter.” 

4.9. The observation that aroused 
the interest of the investigators was 
that although the majoritj’- of alpha 
p.articles in passing through a thin 
sheet of metal either continued in their 
original direction of motion or were 
scattered, i.e., deflected, to a slight ex- 
tent, a small proportion of the particles 
were deflected through large angles, 
some even emerging on the side of inci- 
dence. In a detailed study of the scat- 
tering of the fast-moving alpha parti- 
cles, IT. Geiger and E. IMai-sden (1909) 
reported that when the radiations 
emitted bj' the radioactive element 
radium C impinged on a thin sheet of 
platinum, about one particle in 8000 
was scattercd at an angle of 90° from 


the direction of incidence. “If the high 
velocity [about 1.8 X 10® cm. per sec.] 
and mass of the alpha particle be taken 
into account,” they said, “it seems sur- 
prising that some of the alpha particles 
. . . can be turned within a lajmr of 
6 X 10-® cm. of gold through an angle 
of 90°, and even more.” * To produce 
the same effect by a magnetic deflec- 
tion of the alpha particle would have 
required a field of enonnous magni- 
tude. In his lectures on the Background 
to Modem Science, given in 1936, Ruth- 
erford described the unexpected nature 
of the results in the followdng words: 
“It was about as credible as if you had 
fired a 15-inch shell at a piece of tissue 
paper and it came back and hit you.” 

Rutherford’s Nuclear Atom 

4.10. The first interpretation of the 
large-angle scattering of alpha particles 
was that it wms due to a succession of 
deflections through small angles, aU in 
the same general direction. However, 
in his classical paper of 1911, in which 
he laid the foundation of the modem 
theory of atomic structure, Rutherford 
showed that it was highly improbable 
that this was the case. In view of J. J. 
Thomson’s model of the atom as con- 
sisting of a number of electrons moving 
in a uniform sphere of positive electrifi- 
cation, it appeared possible that alpha- 
particle scattering might be due to en- 
counters with the electrons. But, said 
Rutherford, “remembering that the 
mass, momentum and kinetic energy of 
the alpha particle are veiy large com- 
pared ^vith the corresponding values 
for the electron . . . , it does not seem 
possible . . . that an alpha particle 
can be deflected through a large angle 
bj’’ a close approach to an electron.” 


tinno^'ooici’'r*’A!v) Jaboraton' and at whose suggestion the work was 

5 in ’'’a OOe « cn. ^ ^ small Iraction of incident alpha particles, about 

poll;* T ! k averap angle of 90' in p:issing through a thin layer of 

rc!>orl of OcigeV .and ^ >^sult does not appear in the published 





on Atomic Energy Chap IV 


t’j'* oumb<?r of uait ^isrcs? C 2 the tar- 
nucleus, 13 taken s* co that Uie 
atomic ww^ht is is tb» r®o g of 40, it 
» found from eqea:.^ \i I) that do is 
about 10““ era 'll:- raars* the tar- 
get nucleus, whiA ran:* be le^s than 
tlus figure, «hpJd thii: be the order 
of 10*‘Mo lO-^cm 
410 In addition to the method 
ba<!cd on the «!C3}terinc of alpha parti- 


cles, ttt 0 procedure' h3n> been used lo 
mdic'itc the dimensions of atomic nu- 
clei One i» related to the behavior of 
ndioictive elements emittme alpha 
(5735), vii the other m 
lohMi'tudl ofthcwttcrmeofhigh- 
rnrrn neutrons (§ HIM It 

|« csi>«lc<t Hist 'I't' 

fhouW P' c lh« rt 

a,,tl,<,ntoni.cnucleusBt>OTtJl h»‘>t 

tin hittilj lie rtptrdcd ns im entity of 

ilcfmito site Neterlhticss, It ”PP«^ 


I account for nuclear masses, the neu- 
tron cames no charge and so its ma^ 
cannot be electromagnetic m nature 
4>2i, The radius of an atom is about 
10^ cm (§ 1 65), and since it consists 
of a single central nucleus, with a radius 
of the order of 10““ cm or less, and a 
relatively small number of electrons, 
each of which has a radius of 2 X 10~“ 
cm , it IS obvious that an atom must 
have a ver> "empty” structure For an 
atom with a (positive) nuclear charge 
of 20 for example, there are 20 (nega* 
tive) electrons outside the nucleus 
I since the atom as a whole is neutral 
The total volume of the nucleus and 
the electrons m a single atom is calcu 
lated to be about 10“*® cc , compared 
with the total effective volume of ap- 
proximately 10“®^ cc for the atom as 
a whole To the eictent that nuclear 
and electronic volumes have any real 
significance — because of the operation 
of the uncertainty principle — it would 
appear that the actual volume of ma 
tenal, i e , of the nucleus and the elec 
Irons present m an atom is only about 
I0"« of the effective atomic volume It 
is not surprising therefore, that fact 
moving electrons, e g , beta particles 
and alpha particles, can so easily pass 
through appreciable thicknesses of 
matter 


The Nucueah Chauob 
4 22 Because of experimental difF 
culties the accuracy of the scatterin 
measurements made by Geiger an 
Marsden, referred to above was sue 
as to give the value of the nuclei 
charge with a possible error of some 2 
per cent As already mentioned, a! 
*y n* could be said was that the numbe 
iitnry positive charges on tBi 
was approximately half lb 
’ *' Tlira result was m gen 
nth a conclusion pre 
C G Barkla (ISlD 



neutral, the positi%’'e charge on the nu- 
cleus must be balanced by an equal 
number Z of negative charges in the 
form of electrons. It follows, therefore, 
that the number of electrons is roughly 
half the atomic weight, and hence 
would not greatly exceed 100 even for 
the heaviest elements. Further, since 
the mass of an electron is roughly a 
two-thousandth part of that of a hy- 
drogen atom, the maximum number of 
about 100 electrons would represent no 
more than a tw'entieth of the mass of a 
hydrogen atom, i.e., 0.05 on the ordi- 
nary' atomic weight scale. It is obvious, 
therefore, that essentially the whole of 
the mass of an atom, as well as all of its 
positive charge, must be concentrated 
in the nucleus. 

4.15. According to Hutherford’s cal- 
culations, the gi'eater the angle through 
which an alpha particle, has been de- 
flected, the closer has it approached the 
atomic nucleus before being turned 
back. By determining the maximum 
scattering angle, the distance of closest 
approach between the centers of an 
atomic nucleus and an alpha particle 
may be calculated. This distance, 
which is found to be of the order of 
10~^' cm., represents a maximum value 
for the sum of the radii of an atomic 
micleus and an alpha particle. Since 
the alpha particle is itself the nucleus 
of a helium atom, as will be seen below 
(§ 4.30), it is evident that the radius of 
an atomic nucleus is somewhere be- 
tween lO-i- and 10-» cm. 

4.10. An approximate evaluation of 
the size of the target nucleus* may be 
made in the following manner. As 
.“^hown in § 2.103, an alpha particle car- 
ne.s two (positive) unit charges, i.e., 2c, 
and since the (positive) charge on the 
nurlfu.s is Zc, wirerc Z is approximately 
half the atomic weight, the force of re- 
Ths; t<'rm micleas’' 


The Structure of the Atom 89 

pulsion between the target nucleus and 
an alpha particle when their centers are 
at any distance d apart is given by 
Coulomb’s law as 2e X Zefd?, i.e., 
2Ze^ld-. The potential energy or work 
of repulsion is obtained by integration 
over all distances from infinity to d, 
and the result is found to be 2Ze^fd. 

4.17. Suppose that an alpha particle 
of mass m, moving with a velocity v, 
and hence having a kinetic energy 
is approaching the atomic nu- 
cleus along the line joining their cen- 
ters. As the particle gets closer the 
potential energy of repulsion increases, 
since d is continually diminishing; 
eventually a point is reached when this 
energy'- {2Ze^fd) just balances the ki- 
netic energy with which the 

alpha particle is moving toward the 
nucleus. At this point the alpha parti- 
cle comes to rest instantaneously’- and is 
then turned back. The distance da of 
closest approach between the target 
nucleus and the alpha particle may 
consequently be derived by equating 
the repulsive potential energy 2Ze-lda 
to the kinetic energy of the alpha 
particle; thus, 


so that 


2Ze^ 
da " 

da = 


mv^ 


iZe\ 

miP 


(4.1) 


4.18. The electronic charge e is 
known to be 4.80 X IQ-^Oe.s.u. (§2.41), 
and the mass of the alpha particle, 
which is virtually identical with that of 
a helium atom, is obtained by dividing 
the atomic weight of helium, 4.00, by 
the Avogadro number, 6.02 X 10^ 
(§ 1-64), The average velocity of an 
alpha particle may be taken to be 
about 1.5 X 10’ cm. per sec., and if Z, 



90 


Sourcebook on 

the number of unit charges on the tar- 
get nucleus, is taken as 20, so that the 
atomic weight is in the region of 40, it 
IS found from equation (4 1) that do la 
about 10”“ cm The radius of the tar- 
get nucleus, which must be less than 
this figure, should thus be of the order 
of 10-“ to 10-“ cm 
4 19 In addition to the method 
based on the scattering of alpha parti- 
cles, two procedures have been used to 
indicate the dimensions of atomic nu- 
clei One is related to the behavior of 
radioactive elements emitting alpha 
particles (§7 32), and the other in- 
volves a study of the scattenng of high- 
energy neutrons (§ 11 105) It is not to 
be expected that the different methods 
should give the same results, especially 
as the atomic nucleus is so small that it 
can hardly be regarded as an entity of 
defimte size Nevertheless, it appears 
that nuclear radii, especially for ele- 
ments of higher atomic weight, may be 
represented by the foimula 1 5 X 10*-“ 
A*''® cm , where A is the atomic weight, 
or mass number (§ 8 58), of the ele- 
ment concerned On the basis of this 
relationship, the nuclear radii of natu- 
rally occurring elements range from 
about 1 5 X 10”“ cm for hydrogen to 
9 X 10”“ cm for uranium 
4 20 It will be recalled that the ra- 
dius of an electron is about 2 X 10”“ 
cm (§ 2 59), so that atomic nuclei, m 
spite of being many thousand times 
heavier than an electron, are not very 
different m radius It was thought at 
one time that the nuclear mass was 
essentially electromagnetic in nature, 
bemg like that of the electron, due to 
its electric charge If this were iJie 
case, nuclear radii would be \ery much 
smaller than are actually found Con- 
sequently, the mass of the nucleus is 
governed by factors other than the 
charge As will be seen below, it is the 
presence of protons and neutrons whidi 


Atomic Energy Chap IV 

account for nuclear masses, the neu- 
tron carries no charge and so its mass 
cannot be electromagnetic in nature 
4 21 The radius of an atom is about 
10"* cm (§ 1 65), and since it consists 
of a single central nucleus, with a radius 
of the order of 10”“ cm or less, and a 
relatively small number of electrons, 
each of which has a radius of 2 X 10-“ 

I cm , It is obvious that an atom must 
have a very “empty ’ structure For an 
atom with a (positive) nuclear charge 
of 20, for example, there are 20 (nega- 
tive) electrons outside the nucleus, 
since the atom as a whole is neutral 
The total volume of the nucleus and 
the electrons in a single atom is calcu- 
lated to be about 10^® cc , compared 
with the total effective volume of ap- 
proximately cc for the atom as 
a whole To the extent that nuclear 
and electronic volumes have any real 
significance — because of the operation 
of the uncertainty principle— it ■would 
appear that the actual volume of ma- 
tenal, i e , of the nucleus and the elec- 
trons, present m an atom is only about 
10*-“ of the effective atomic volume It 
IS not surprising, therefore, that fast- 
movmg electrons, e g , beta particles, 
and alpha particles, can so easily pass 
through appreciable thicknesses of 
matter 

Tee Nuclear Charge 
4 22 Because of experimental diffi- 
culties, the accuracy of the scattenng 
mei^rements made by Geiger and 
Maraden referred to above was such 
os to give the value of the nuclear 
charge with a possible error of some 20 
per cent As already mentioned, all 
that could bo said was that the number 
of elementary positive charges on the 
nucleus was approximately half the 
atomic weight 'Hus result was in gen- 
eral agreement with a conclusion pre- 
viously reached by C G Barkla (1911) 



91 


The Struciure of the Atom 


ns a result of his experiments on the 
scattering of X-rays. According to a 
theoretical treatment by J. J. Thomson 
(1906), the extent of the scattering is 
determined by the number of electrons 
in the atom, and Barkla found tliis 
number to be roughly half the atomic 
weight for several light elements. The 
number of electrons in an atom should, 
of course, be equal to the number of 
unit positive charges on the nucleus. 


Broek is accorded priority for the first 
publication of the view that has be- 
come universally adopted. It may be 
noted that for the lighter elements, up 
to molybdenum, at least, the atomic 
number is within about 10 per cent of 
half the atomic weight. The approxi- 
mate estimates of the nuclear charge 
and of the number of electrons, made 
by Geiger and Marsden from alpha 
particle scattering and by Barkla from 



Fig. 4.2. Moseley’s photograph of char- 
acteristic X-rays of consecutive elements. 


4.23. Early in 1913, the Dutch 
physicist A. van den Broek, in a paper 
on Eadiodanents, the Periodic System 
nnd the Constitution of the Atom, made 
the suggestion that the number of posi- 
tive charges on the nucleus of any 
given .atom iscipial to the ordinal num- 
ber of the particular element in the pe- 
riixlic system, now ixjferred to as the 
atomic numlier (§ 1.44). The same idea 
must have been in the minds of K. 
Fajans in Germany and of F. Soddy in 
Great Britain (§ S.9), but van "den 


X-ray scattering, respectively, thus 
agreed fairly well rvith the suggestion 
that they should be equal to the atomic 
number of the element. 

4.24. The next important step in 
connection with the determination of 
the magnitude of the nuclear charge 
was taken in 1913 in Rutherford’s 
hlanchester laboratory, by the young 
English physicist H. G.-J. Moseley, 
who was killed two years later in the 
battle of Gallipoli. Utilizing the then 
recent discover}' that a crj'-stal could 




92 Sourcebook on Atomic Energy 

act as a diffraction grating, and hence 
could be used to compare the wave 
lengths of X-rays (§ 2 91), Moseley 
made a study of the charactenstic 
X-rays (§ 2 86) of a number of ele- 
ments A photographic method was 
used, so that the positions of the lines 
on the plate were du-ectly related to the 
wave lengths of the particular X-rays 
The results obtained for a senes of con- 
secutive elements in the penodic sys- 
tem, from calcium to zinc — mth the 
exception of scandium, which follows 
titamum — are shown m the historic 
photograph in Fig 4 2 It is apparent 
that the wave lengths of the character- 
istic X-rays change m a regular manner 
with mcreasmg atomic number of the 
element 

4 25 From the positions of the Imes, 

Moseley determined the frequencies 
(§ 3 13) of the corresponding radia- 
tions, and then calculated a quantity, 
to winch he gave the symbol Q, that 
was related to the square root of the 
frequency of the characteristic X-rays 
for each element Upon examimng the 
results he remarked “It is at once evi- 
dent that Q increases by a constant 
amount as we pass from one element to 
the next, using the chemical order of 
the elements m the periodic system 
we have here a proof that there is 
m the atom a fundamental quantity, 
which mcreases by regular steps as we 
pass from one element to the next 
This quantity can only be the charge 
on the atomic nucleus ’’ 

4 26 After, referring to the conclu- 
sions drawn from alpha particle and 
X-ray scattering, that the number of 
umt charges on the nucleus of any atom 
is approximately half its atomic weight, 

* This IS the first mention of the term atomic nitmlw, for the ordinal number of an element 
m the peno^e system, the present author has been able to find, although as long ago bs 
1864, JAR Newlands (see § 1 40) employed the expression “the number of the element 
for this quantity Wnters in the German language used the word ' Ordnungszahl," which 
means “ordinal number “ , , . . i, , 

t It 13 even becoming the practice to define the atomic number of an element as the number 
of uEUt positive chaiges earned by the ntielens 


Chap IV 

Moseley went on to say “Now atomic 
weights mcrease on the average by 
about two umta at a time, and this 
strongly suggests the view that the 
. . . [number of charges] mcreases 
from atom to atom by a single elec- 
tronic umt We are therefore led by 
experiment to the view that . . . [the 
number of charges] is the same as 
the number of the place occupied by the 
element m the periodic system This 
atomic number* is then for hydrogen 
1, for helium 2, for lithium 3, . . for 
calcium 20, . for zme 30, etc ” 

4 27. The work desenbed above was 
interrupted by World War I, but after 
the war, James Chadmek (see § 2 110), 
m Rutherford's laboratory at Cam- 
bridge, England, set out to make an 
accurate study of the scattenng of 
alpha particles with a view to calculat- 
mg the number of unit charges earned 
by an atomic nucleus From his meas- 
urements, reported m 1920, he esti- 
mated the nuclear charges of copper, 
silver and platinum to be 29 3, 463 
and 77 4 units, respectively, with an 
accuracy of between 1 and 2 per cent 
These figures are in excellent agree- 
ment with the respective atomic num- 
bers of 29, 47 and 78 Similar accord 
was obtained by P Auger and F Per- 
no (1922) m France for argon, by E S 
Bieler (1924) m England for idummum 
and magnesium, and by Rutherford 
and Chadwick (1925) for gold 
4 28 As a result of these observa- 
tions, and of many others, it is now un- 
questioned that the number of unit 
positive charges earned by the nucleus 
of any atom is equal to the atomic 
number of the particular element t 
The number of electrons surrounding 



93 


The Structure of the Atom 


the nucleus and maintaining electrical 
neutrality of the atom as a whole, fre- 
quently referred to as the exlranuclear 
electrons or orhitnl electrons, must conse- 
quently also be equal to the atomic 
number. For this reason the symbol Z 
is used to represent both the atomic 
number, or the nuclear charge, and the 
number of the orbital electrons associ- 
ated mth the atom of a given element. 

4.29. It follows, as a consequence of 
the foregoing arguments, that in the 
hydrogen atom the nucleus carries a 
single positive charge and there is one 
e.xtranuclear electron ; the helium atom 
has a nucleus udth two positive charges 
and there are two external electrons; 
the nucleus of the lithium atom carries 
three positive charges and there are 
three surrounding electrons, and so on 
throughout the periodic system. Tire 
heaviest naturally occurring element, 
uranium, has an atomic number of 92; 
thu.s, its nucleus has 92 positive charges 
and there arc the same number of ex- 
tranuclcar electrons. 

4.30. The proton, as seen in § 2.64, 
has the same mass as a hydrogen atom 
and carries a single positive charge; 
hence, it is equivalent to such an atom 
which has lost one unit negative charge, 
i.c., one electron. As the hydrogen 
atom contains but a single electron, it 
is evident that the proton is identical 
with .a hydrogen nucleus. Similarly it 
will be readily apparent that an alpha 
particle is actually a helium nucleus, 
that is, a helium atom minus its two 
electrons, so that it carries two positive 
charges. 

4.31. It may be remarked that in the 
process of ionization, whereby an atom 
or a group of atoms acquires an electric 
charge and hence becomes a carrier of 


electricity, the orbital electrons are in- 
volved. If by some means, such as an 
electrical discharge or by the action of 
alpha or beta particles, one or more 
electrons are removed from an atom, or 
a molecule, the result is a positive ion. 
Thus a proton is a singly-charged, posi- 
tive hydrogen ion, while an alpha par- 
ticle is a doubly-charged, positive he- 
litun ion. On the other hand, when an 
atom or molecule acquires in some 
manner one or more additional elec- 
trons, which have been ejected from 
other atoms or molecules, a negative 
ion is formed. As a general rule, an 
iom-pair consisting of a positive and a 
negative ion or, more commonly, of a 
positive ion and an electron, is pro- 
duced in every ionization act in a gas.* 

The Strtjcttoe of the Nucleus 

4.32. The problem of the structure 
of the atom thus divides itself into two 
virtually distinct parts: first, a consid- 
eration of the small, central nucleus 
wluch carries the positive charge and 
essentially the whole mass of the atom, 
and second, the arrangement of the 
extranuclear or orbital electrons within 
the considerably larger space available 
to them. The former aspect will be 
dealt with somewhat briefly here, but 
it ^vill be taken up again later (§ 4.77) 
when further information has been 
presented. 

4.33. Since the lightest positively 
charged particle known before 1932 
was the proton,! it was naturally as- 
sumed that atomic nuclei w'ere built up 
of a system of closely-packed protons. 
The mass of the proton is approxi- 
mately unity on the ordinary atomic 
weight scale and it carries a single posi- 
tive charge. In order to account for the 


“ion-pair” should not bo confused with “positron-electron" pair, described 



94 


Source&oofc on 

mass of a nucleus of atomic weight A, 
it was therefore necessary to suppose 
that it contained A protons However, 
if this were the case, the number of unit 
positive charges on the nucleus would 
be the same as the atomic wej^t, 
whereas it has been sho^vn to be equid 
to the atomic number Z, which is half, 
or less, of the atomic weight It was 
suggested, therefore, that, m addition 
to protons, atomic nuclei contained 
A — Z (negative) electrons, these 
would contnbute a negligible amount 
to the total mass, but would make the 
net positive charge, i e , A — (A — Z) 
=s Z, equal to the atomic number, al- 





Atomic Energy Chap IV 

tioned m § 2 109, that a neutral combi- 
nation of a proton and an electron, 
called a neutron, might exist as a con- 
stituent of atomic nuclei 
4 35 After the discovery of the neu- 
tron m 1932, W Heisenberg (see § 3 45) 
immediately came forward with the 
idea that the nucleus contains only 
protons and neutrons, he showed, by 
means of wave mechanics, that the at- 
tractive forces existing between these 
elementary particles would be suffi- 
cient to account for the existence of 
stable nuclei The theory was modified 
and improved m 1933 by the Italian 
phj^icist E Ma]orana, and this has 



8t B c 

/(>$ 

/•4 /•» 


Fio 4 3 Pictorial representation of neutrons (n) and protons (+) m 
simple atomic nuclei 


though the total number of protons 
(A) would be the same as the atomic 
weight 

4 34 The view that electrons, as 
well as protons, were present in atomic 
nuclei appeared to receive support from 
the fact that beta particles, i e , elec- 
trons, are emitted by certain radioac- 
tive elements, presumably from the 
nuclei of their atoms Nevertheless, 
the stability of a closely packed sj stem 
of protons and electrons was difficult to 
explain, and various other possibilities 
were considered from time to time 
Among these was the suggestion, made 
independently, and almost simultane- 
ously in 1920, by three scientists in 
different parts of the world, as men- 


formcd the basis of modem views on 
nuclear structure Because thej are 
the essential constituents of atomic 
nuclei, neutrons and protons are often 
referred to by the general name of 
mtckon * 

4 36 The mass of a neutron, hke 
that of a proton, is close to umty on the 
atomic weight scale Hence, an atomic 
nucleus, of atomic weight A and atomic 
number Z, contains A nucleons, con- 
sisting of Z protons and A — Z neu- 
trons Some pictonal representations 
of Uie structures of a few of the simpler 
atomic nuclei are shown in Fig 4 3 In 
ordinary hydrogen, atomic weight 
A — 1, and atomic number Z = 1, the 
nucleus consists of a smgle proton, as 


•The term "nuclon” was onginally proposed by F J Belinfante m Holland in 1939 
but this was dianged to "nucleon,^ for etyni<Hogical reasons and used by the Danish physicist 
C Mpller m 1941 The use of the word nudeomcs ’ to describe the general field of nuclear 
science and technology, was proposed by Z Jeffries m July 1944 



95 


The Structure of the Atom 


stated above; in helium, A = 4 and 
2 = 2, the nucleus contains two pro- 
tons and two neutrons; the nucleus of 
the carbon atom (A = 12, Z = 6) is 
made up of six protons and six neu- 
trons, and so on. 

4.37. For elements of low atomic 
weight, the atomic number Z is approx- 
imately half the atomic weight A; 
atomic nuclei of such elements thus 
contain almost equal numbers of neu- 
trons and protons. With increasing 
atomic weight, the atomic number Z 
becomes less than half of A; hence 
A — Z is greater than Z, and the num- 
ber of neutrons in a stable nucleus ex- 
ceeds the number of protons. The 
atomic weight of uranium, for example, 
is 238 and its atomic number is 92, so 
that the nucleus consists of 92 protons 
and 146 neutrons. It will be seen in 
Chapter XII that these facts are im- 
portant in trjdng to undemtand the 
factors which contribute to the stabil- 
ity of atomic nuclei. 

4.38. There is one further point to be 
considered. If nuclei consist essentially 
of neutrons and protons, both of which 
have masses of almost unity, then the 
atomic weights of all elements should 
be very close to whole numbers. As 
stated in § 1.39, in connection vdth 
Front’s 115 ^) 0 ^ 10815 , a surprisingly large 
proportion of the elements do in fact 
have atomic weights which differ from 
integral values by no more than 0,1. 
The apparent exceptions are due to 
the fact that. man 5 ' elements actually 
consist, of mi.xtures of atoms of different 
atomic weights, so that the average is 
not a whole number. Chlorine, for ex- 
ample, contaim? atoms with atomic 
weights clo.so to 35 and 37, and they^ 
are present in such proportions as to 
give an average value of 35.46. This 
matter will be understood more clearl}' 


when the concept of "isotopes” has 
been discussed in Chapter VIII. In the 
meantime, it may be mentioned that if 
the protyle, which Front thought to be 
hydrogen, were extended so as to in- 
clude both protons and neutrons, the 
h 5 ’pothesis, which he put forward on so 
little evidence over a hundred years 
ago, would be accepted at the present 
day. 

Stability of the 
Alpha Pabticle 

4 . 39 . Since alpha particles, i.e., he- 
lium nuclei of mass 4.00, are ejected 
from the nuclei of several radioactive 
elements, and since the nuclei of ele- 
ments whose atomic weights are multi- 
ples of four are known to be exception- 
ally stable (§ 12.26), it was thought 
possible that alpha particles might be 
secondary imits of nuclear structure. 
Since helium has an atomic weight very 
close to 4 and an atomic number of 2, 
its nucleus wvould consist of two pro- 
tons and two neutrons, as seen above. 
Such a combmation would be expected 
to have great stability. One way of 
seeing that this must be so, is to ex- 
amine the weights of the alpha particle 
and of its constituent nucleons. The 
mass of a proton is 1,00758 and that of 
a neutron is 1,00897,* so that the total 
mass of the constituents of an alpha 
particle would be as follows: 

Mass of two protons h 
= 2 X 1.00758 ( 

Mass of two neutrons ? ~ -0331. 
= 2 X 1.00897 ) 

4.40. The actual mass of an alpha 
particle, i.e., a helium nucleus, obtained 
by subtracting the mass of two elec- 
trons from that of the helium atom, is 
4.0028. There is consequently a de- 


physical atomic weight scale which wiU be explained 



96 


^fourcc&ooi on Atomic Energy 


crease of mass, and hence a liberation 
of energy (§ 3 76), in the formation of 
an alpha particle from its constituent 
nucleons The loss of mass is 4 0331 — 
4 0028 , 1 e , 0 0303 atomic weight units, 
and by equation (3 22), based on the 
Einstein mass-energy relationship, this 
IS equivalent to 28 2 Mev Hence, m 
the formation of a single alpha particle 
from two protons and two neutrons, 
the considerable amount of 28 2 Mev 
of energy, referred to as the binding 
energy, will be released Conversely, if 
it were required to break up an alpha 
particle into its constituent nucleons, 
this same large quantity of energy 
would have to be supplied This 
means that the alpha particle is ex- 
tremely stable, as implied above 
4 41 Although the combination of 
two protons and two neutrons has ex- 
ceptional stability, it is believed at the 


Chap IV 

present time that the alpha particle is 
not generally found m atomic nuclei 
According to a theory developed by W 
Elsasser m 1934, alpha particles could 
only exist in the nuclei of other atoms 
if the radius of the alpha particle were 
small compared with the distance be- 
tween the particles m the nucleus Ac- 
tually, these distances would be much 
the same, so that the condition for the 
presence of alpha particles as second- 
ary units of nuclear structure is not 
satisfied "When, as is the case with 
some radioactive elements, the circum- 
stances are such that the binding en- 
ergy of the alpha particle, as calculated 
above, exceeds the amount of energy 
required to remove two protons and 
two neutrons individually from the 
nucleus, an alpha particle can be 
ejected, although it is not really pres- 
ent as such m the nucleus 


THE EXTRANUCLEAR (ORBITAL) ELECTRONS 


Atomic Spectra 

4 42 A great deal of information 
concerning the arrangement of the 
electrons surroimding atomic nuclei 
hag been obtained from the study of 
atomic spectra When a substance is 
heated sufficiently strongly in a flame 
or by means of an electric arc or spark, 
or, if it IS gaseous, an electrical dis- 
charge IS passed through it, radiation, 
mainly in the visible and ultraviolet 
range, is often emitted If the rays are 
examined in a spectroscope, which is an 
instrument for splitting up complex 
radiation into its components of differ- 
ent wave length, a definite pattern of 
lines, known as a spectrum, appears 
This spectrum is characteristic of the 
element or elements present m the ma- 
terial emitting the radiations, it is usu- 
ally called an atomic spectrum, since it 
originates in the atom of the element 


The lighter atoms, such as hydrogen 
and helium, yield fairly simple spectra, 
with a relatively small number of lines, 
but for some of the heavier atoms the 
^ectra may consist of hundreds of 
Imes As a result of much painstaking 
work, the wave lengths of the spectral 
hoes of most elements are now known 
with considerable accuracy, and vari- 
ous numerical relationships have been 
discovered to exist among them These 
have proved of great value in the con- 
struction of a theory of atomic spectra, 
which 13 closely related to the problem 
of the extranuclear electrons 
4 43 Accordmg to Maxwell's elec- 
tromagnetic theory of light (§ 3 23), 
the emission of radiation, such as the 
characteristic spectrum of an element, 
IS due to an oscillating electncal sys- 
tem Concurrently with the growth of 
the concept of the electron as the unit 



The Structure of the Atom 97 


of charge, there was the parallel devel- 
opment of the idea that these spectra 
were related to a vibrating electronic 
charge wthin the atom. Suggestions 
of this kind were made in the early 
1890s by several scientists, including 
G. J. Stoney, G. F. Fitzgerald, H. 
Ebert, and, in particular, J. Lannor 
(1894) and H. A, Lorentz (1895) who 
treated the mathematical aspects of 
the problem in some detail. Even be- 
fore the publication of J. J. Thomson’s 
work wliich established the existence of 
the electron as a definite entity, the 
Lorentz theory was used to explain the 
effect of a magnetic field in splitting 
spectral lines as observed by P. Zeeman 
(1896). This, somewhat fortuitously, 
led to a value of the specific charge of 
the electron, as stated in § 2.55, in 
agreement with that derived by more 
direct methods. 

4.44. IMien Nagaoka proposed liis 
Saturnian atom (§4.6) he suggested 
that atomic spectra might be due to 
"the oscillatory motion of electrons re- 
volving in circular orbits,” but this 
view was untenable, as will be seen 
from the following arguments. To ac- 
count for the fact that electrons did 
not fall into the positivelj’’ charged nu- 
cleus as a result of electrical attraction, 
Rutherford found it necessai^’- to postu- 
late a rapid rotation of the electrons 
aro\md the nucleus, somewhat similar 
to the rotation of pkanets around the 
sun. The inward attractive force wms 
supposed to be balanced by the out- 
ward centrifugal force. However, the 
analogj' between an atom and the sun’s 
planetary' system is fallacious, because 
the particles in the atom are electri- 
cally charged. By the electromagnetic 
thcorj', the rotating electron should 
continuously emit energj- as radiation 
during its motion, but if this were the 
ca.'ie the radius of cunmture of its orbit 
would steadily diminish. The electron 


would thus follow a spiral path and 
eventually fall into the nucleus. Fur- 
ther, if the spectrum %vere related to 
the energy radiated by the moving 
electron, this energy wmuld be chang- 
ing wdth the radius of curvature of the 
path. Atomic spectra would thus cover 
a continuous range of wmve lengths in- 
stead of consisting of well defined lines. 

Bohr’s Theory of 

Stationary States 

4.46. In order to overcome these 
difficulties, the Danish phj^sicist, Niels 
Bohr, then working in Rutherford’s 
Manchester laboratorj’’, made in 1913 
the surprising suggestion that, con- 
trarj' to the requirements of classical 
electromagnetic theory, an electron 
does not radiate energy while it is mov- 
ing in a closed orbit. Such an orbit 
W'ould consequently be stable, and it 
w'ould represent -what Bohr called a 
sMiomry state of the atom. It was 
postulated that several stationary 
states were possible, the energy being 
constant in each state, but differing 
from one state to another. The pro- 
duction of a spectral line, of definite 
frequency wms then attributed to the 
radiation of energy associated wdth the 
transition or “jump” of an electron 
from a state of higher energy to one of 
lower energy, the frequency (or wmve 
length) being related to the energy 
change hy means of the quantum the- 
ory equation. 

4.46. If Fj is the energy of the atom 
in a state of higher energy (initial state) 
and El is the value in the state of lower 
energj’ (final state), then an electronic 
transition from the former to the latter 
state %vill be accompanied by the emis- 
sion of energ}^ Ez — Ei. By Planck’s 
quantum theorj^ equation (3.2), it fol- 
lows that the frequency v and w’ave 
length X of the corresponding spectral 
line are given by 



98 


Sourcehooh on Atomic Energy Chap IV 


h 


he 


V Ei — El 


( 42 ) 
(4 3) 


where h is Planck's constant and c is 
the velocity of light Each particular 
energy transition, from one state to an- 
other, should thus result m the formar 
tion of a spectral Ime whose frequency, 
or wave length, is given by equation 
(4 2), or (4 3) Since several different 
stationary states are possible in every 
atom, there should be a number of 
transitions and hence a senes of lines 
should be observed in the spectrum 



Fio 4 4 Transitions of electrons from 
I higher to lower energy states giving spectral 
lines 

4 47 If a substance is exposed to 
conditions under which the absorption 
of energy is possible, e g , by the use of 
iugh temperattme or a suifabte efectn- 
cal discharge, the electrons which are 
normally m their lowest energy state, 
or ground state, are presumed to take up 
energy and to pass into states of higher 
energy These are known as excited 
states of the atom The spontaneous 
return of the electrons from the higher 
♦o the lower states should result in the 
liberation of specific amounts of en- 
ergy, each such transition giving a Ime 
of definite frequency (or wave length) 
in the spectrum (Pig 4 4) Since many 
different energy states are possible in 


every atom, numerous lines may be ob- 
served It might be imagined that the 
spectra of atoms of high atomic num- 
ber, which have a large number of elec- 
trons, would give extremely complex 
spectra This is not altogether true, 
for it has been established that only a 
few — usually one, two or three — of the 
outermost electrons are concerned m 
the formation of ordinary, or optical, 
spectra However, even this small 
number is sufficient to introduce many 
I complications 

I 4 48 The energy differences of sue- 
I cessive electronic states involved m the 
; formation of optical spectra can be de- 
termined directly m some instances 
and the values have been found to be 
of the order of 1 to 10 electron volts 
(§ 3 81) The frequency or wave length 
of the corresponding radiation can be 
calculated by means of the quantum 
theory equations (4 2) or (4 3), respec 
lively, or more directly by the equiva- 
lent equations (3 18) and (3 19) or 
(3 20) If for example, the difference 
of energj between o electronic states 
involved m a particular transition is 2 
ev, I e , 2 X ICH Mev, it follows imme- 
diately from equation (3 20) that the 
wave length of the emitted radiation 
should be 0 62 X 10~* cm or 6200 A 
Tins would represent a line m the visi- 
ble region of the spectrum (§ 3 16) A 
/arger value ci the energy difference 
would mean a shorter wave length bo 
that the spectral Ime might appear in 
the ultraviolet region 
4 49 According to the accepted 
ideas of the time, Bohr’s approach u as 
somewhat contradictory, for he had to 
make t^vo assumptions first, to use his 
own words that “the d5Tiamical equi- 
hbnum of the systems in the stationary 
states can be discussed by help of the 
ordinary mechanics [and second, 
that] the passing of the systems 
betiveen different stationary states 



99 


The Structure of the Atom 


. , . is followed by the emission of a 
homogeneous radiation, for which the 
relation between the frequency and the 
amoimt of energy emitted is the one 
given by Planck’s theory. . . . The 
second assumption is in obvious con- 
trast to the ordinary ideas of electro- 
dynamics, but appears to be necessary 
in order to account ‘for the experimen- 
tal facts.” Bohr’s justification was 
consequently that atomic spectra could 
not be correlated wth the nuclear atom 
in any other way. 

4.B0. By assuming further that the 
electrons moved in circular orbits and 
that the angular momentum mvr — 
where m is the mass of the electron, and 
V is its velocity in the orbit of radius r — 
is gmniieed, that is to say, it is re- 
stricted to certain values which are in- 
tegral multiples, e.g., 1, 2, 3, . . . , n, 
of a definite quantum, Bohr w'as able 
to evaluate the energies for the possible 
stationary states of the hydrogen atom. 
Upon inserting these results in equa- 
tion (4.2) or (4.3), the frequencies or 
wave lengths of the lines in the hy- 
drogen spectrum Avere determined and 
found to be in remarkable agreement 
AAoth the experimental values. This 
agreement represented a great triumph 
for Bohr’s theorj', in spite of its founda- 
tion upon postulates which appeared 
to conflict with each other. 

Quantum NctiIbers 

4.61, Tlie energj' values calculated 
for the various possible stationary 
states w’cre found to be dependent on 
the integral multiples of the momen- 
tum referred to above; hence, each 
postulated energj’ state could be asso- 
esated with a particular quantum num- 
ber (n). Further, each state corre- 
SjKincled to a definite circular orbit, the 


radius of Avhich was also determined by 
the quantum number; thus, for any 
orbit of quantum number n, Bohr 
showed the radius r„ of a hydrogen 
atom to be given by 

r„ = 0.53 X 10-« X cm. 

In view of subsequent developments in 
wave mechanics (§ 4.56), it has become 
doubtful if these orbital radii have any 
real significance. The value of r for the 
innermost orbit, with n = 1, is seen to 
be 0.53 X 10“® cm., which is very close 
to the accepted value for the normal 
radius of the hydrogen atom. In the 
higher energ^*^ states, i.e., for n = 2, 3 
etc., the apparent orbital radii are seen 
to increase rapidly; thus, 2.12 A for 
71 = 2, 4.77 A for 71 = 3, and so on. 

4.62. In Bohr’s original theory, the 
electron orbits had to be circular, but a 
later modification in 1916, due mainly 
to A. Sommerfeld in Germany, show'ed 
that by introducing a subsidiary quan- 
tum number, usually called the azi- 
muthal quantum number, elliptical as 
Avell as circular orbits became possible. 
This number is related to the angular 
momentum of the electron due to its 
motion around the nucleus. For each 
particular value of the principal quan- 
tum number n, only certain values of 
the azimxithal quantum number I were 
permitted; these varied, by steps of 
unity, from zero to 7i — 1.* Thus if n 
was 4, then I could be 0, 1, 2 or 3, but 
notliing else. The orbit vdth ti = 4 
and I — 3 w'as supposed to be circular, 
but the others were ellipses of increas- 
ing eccentricity as the value of I de- 
creased. With the increased number of 
energj’ states permitted by the addi- 
tional quantum numbers, it was found 
possible to account for the detailed 


Sommcrfcld’s oriRinal treatment tliig suteidSary quantum number was represented bv h 
.. nrrn 'cntn !Mcr ncvriopTncnla on wave tnecKanics, 



100 SourcAooh on 

structure of the lines of the hydrc^en 
spectrum, and also for many of the : 
characteristic features in the spectra , 
of other atoms j 

4 63, Subsequently, a mflffnctiCffMon- j 
turn number m was introduced with per- 
mitted integral values, mcludmg zero, 
ranging from 1 to — I, that is, 3, 2, 1, 0, 
—1, —2, —3 for I = 3, to account for 
the behavior of spectra m magnetic 
fields The different values of m were 
supposed to represent different orien- 
tations m space of the possible circular 
or elliptical orbits 

4 64 Finally, a fourth quantum 
number, the spin quantum number, had 
to be postulated to account for the 
previously unexplained close grouping 
of two, three or more spectral lines 
Apparently every electron possesses a 
property which, in mechanistic terms, 
can best be described as spm Since 
only two directions of spin are possible, 
the Bpm quantum number can have 
two values, and two values only, for 
every combination of the other three 
quantum numbers These will be indi- 
cated by the symbols + and — , to 
imply opposite directions of spin It is 
a curious fact that although the quan- 
tum numbers I, m and n can have vari- 
ous integral values, depending on cir- 
cumstances, the spin quantum number 
IS always Yi, that is to say, it can be 
either -hY or Tor8imphcity,the ^ 
numerical value wU be omitted m 
the subsequent discussion and only the 
sign mil be indicated 

4 66 If the principal quantum num- 
ber n IS 4, there can be four values of I, 
and a total of sixteen m values, each of 
which can be associated with positive 
or negative spin There are thus 32 
possible states, each mth a slightly dif- 
ferent energy, within the same (fourth) 
electronic level Similarly there are 18 
possible states m the third (tt = 3) 
level, and eight in the second (n — 2) 


AUmac Energy Chap IV 

level If transitions could occur be- 
tween all these levels, the- number of 
spectral Imes would be enormous Ac- 
tually, certain transitions are “per- 
mitted,” while others are said to be 
“forbidden,” meaning that the prob- 
ability of their occurrence is large or 
vamshingly small, respectively The 
restrictions thus introduced, by certain 
well defined selection rules, as they are 
called, serve to limit, to a considerable 
extent, the number of lines in the spec- 
trum of any given element 

Wave Mechanics and 
Electhon Oubits 
4 66 Before proceeding to examine 
the consequences of the four quantum 
numbers described above, it is neces- 
sary to sound a note of caution In the 
Bohr theory, and on its subsequent 
modifications, it was assumed that 
both the position, in a defimte orbit, 
and the momentum of the electron are 
known But accordmg to the uncer- 
tainty principle (| 3 45), this is impos- 
sible If the momentum of the elec- 
tron, and consequently its energy, is 
known exactly, then there must be an 
uncertainty with regard to the posi- 
tion of the orbit, and the extent of this 
indcfiniteness is appreciable in com- 
parison with the size of an atom For 
this reason, it was stated above that 
the caJculated radii o! the electros 
orbits of the hydrogen atom are of 
doubtful significance 
4 57. By using the methods of wave 
mechanics which, as seen on § 3 49, 
should always be employed when deal- 
ing with particles of atomic, or smaller, 
dimensions, many of the apparent in- 
consistencies of the Bohr treatment 
have been removed There is no longer 
any necessity to combine classical 
el^trodynamics with quantum me- 
chanics, and there is no need to make 
assumptions nhich were introduced in 



101 


The Strudure of the Atom 


the original theory chiefly because they 
led to correct results. The same equa- 
tions have now been developed in a 
much more consistent manner, and the 
quantiun numbers 7i, I and vi, instead 
of being somewhat arbitrarj’’, emerge as 
a natural consequence. Further, the 
selection rules, which define the per- 
mitted and forbidden electronic transi- 
tions, mentioned above, are readily 
derived: It is true that Bohr had de- 
duced similar rules in a very ingenious 
manner, but the arguments were less 
satisfactor}' than those based on wave- 
mechanical considerations. 

4,68. However, the gain of mathe- 
matical consistencj^ has been accom- 
panied by a corresponding loss in terms 
of physical reality. The stationary 
electronic states of the atom are now 
referred to as its electronic energy levels, 
and the transition from one level to an- 
other is accompanied by emission of a 
spectral line whose frequenej’’ is still 
given by equation (4,2). But whereas 
in the older theory such a transition 
could be pictured as a jump of an elec- 
tron from one orbit to another, this is 
no longer possible. For one thing, it is 
not permitted to think of an electron 
orbit as a specific path in which an 
electron moves round the nucleus. The 
definite orbit has been replaced b}' a 
mathematical function, sometimes re- 
ferred to as an orbital, which represents 
the distribution of the electron in the 
sp.ace occupied by the atom. Some 
UTiters think of the electron as spread 
out into a cloud of electricity rather 
than as a particle, the orbital giving 
the density of the cloud at any location 
within the atom. The altcniative point 
of view, as explained in Chapter III, is 
to regard the electron essentially as a 
particle, and to interpret the orbital as 
determining the statistical probability 
of finding the electron in any given po- 
sition about the nucleus. 


4.69. Although the latter interpreta- 
tion will be adopted here, it is apparent 
that in neither case is there anjiihing 
approaching a finite electron orbit. It 
may be noted that when the quantum 
numbers n and I are such that the state 
is equivalent to a circular orbit of the 
Bohr-Sommerfeld theory, the probabil- 
ity of finding the electron at any point 
is greatest at the distance represented 
by the corresponding Bohr radius. 
However, whereas the older theory re- 
quires the electron to remain at this 
distance, while in that particular en- 
ergy state, wave mechanics implies 
that there is a definite, but smaller, 
probability that it wll be found at 
points both nearer and further from 
the nucleus. When the quantum num- 
bers correspond to elliptical orbits, the 
coiTelation between the older and 
newer theories is less obvious. 

4.60. The purpose of the foregoing 
remarks has been not so much to ex- 
plain the physical significance of an 
electron orbit as to emphasize the diffi- 
culty of providing such an explanation. 
It is still the practice in many elemen- 
tary books to picture an atom as con- 
sisting of a central nucleus with a num- 
ber of electrons moving around it in 
definite orbits, oriented in various di- 
rections in space. If the uncertainty 
principle and wave mechanics have any 
meaning, and it seems reasonably sure 
that they have, then such pictures are 
misleading. Tliey attempt to give re- 
ality to a state of affairs within the 
atom to which, at least at present, no 
reality can be given. Perhaps if these 
atomic diagrams were to be regarded as 
purely sj-rabolic their use might be 
justified; nevertheless, there is always 
the danger that they may be inter- 
preted too literally. 

4.6L It is true that physicists, while 
realizing its limitations, still frequently 
employ the Bohr-Sommerfeld atom 



102 5ourcc6oofc on 

model, because the calculations are 
simpler than those based on wave me- 
chanics The spectroscopist G Herz- 
bei^ has stated “The fact that even m 
wave mechanics each stationary state 
of the atom has a perfectly definite 
angular momentum shows that the 
atom can still be regarded as consisting 
of electrons rotating about a nucleus, 
as m the onginal Bohr theory,” but he 
IS careful to emphasize that *'we must 
not, however, speak of definite orbits ” 

The Patjh Exclusion Principle 
4 62. Both wave-mechanical theory 
and the experimental facts of atomic I 
spectra require the three quantum j 
numbers, designated above by the let- 
ters n, I and m, to descnbe each energy 
level of an atom In addition, the facts 
indicate the necessity of the spin quan- 
tum number s, which also finds a log- 
ical place m wave mechanics It may 
be regarded as established, therefore, 
that as far os is known at present, elec- 
tromo energy levels, which are those 
concerned in atomic spectra, can be 
fully described by means of appropriate 
values of the four quantum numbers n, 
t, m and s Those permitted by wave 
mechanics are the same as were denved 
from the older theoiy as given in § 4 51 
et seq , although they do not necessarily 
have the same physical significance 
4 63, So far nothing has been said 
about the distnbution of the extranu- 
clear (orbital) electrons among the per- 
mitted quantum states or about its 
physical equivalent, that is, the ar- 
rangement of the electrons in space 
The higher the principal quantum 
number n, the more time will the elec- 
tron spend at a further distance from 
the nucleus, and so there is a relation- 
ship between these two aspects of elec- 
tromc distribution Even m 1897, 
when J J Thomson first reahzed that 
the electron might be a universal con- 


Atornic Energy Chap IV 

stituent of matter (§2 46), he com- 
pared the electrons in an atom to a 
^stem of floating magnets which 
formed a stable system of groups ar- 
ranged in concentric rings Later, m 
1904, when he developed his theoiy of 
atomic structure, Thomson said that 
"the corpuscles [i e , electrons] will 
arrange themselves m a senes of 
concentnc shells ” Furthennore, as 
stated earlier, he realized that there 
must be a connection between the van- 
ation m the properties of elements as 
exemplified by the periodic system and 
the arrangement of the electrons about 
the nucleus In the years 1913 to 1914, 
Bohr, Rutherford and Thomson all 
pointed out that the extranuclear (or- 
bital) electrons, and particularly those 
in the outermost groups or shells, were 
responsible for the chemical properties 
as well os for the spectra of the various 
elements Hence, the problem of the 
arrangement or configuration of the 
electrons around the nucleus became of 
interest to the chemist as well as to the 
spectroscopist 

4 64 Although this problem was es- 
sentially solved by 1924, on the basis of 
a careful study, by many scientists, of 
the chemistry, the optical and X-ray 
plectra, and the magnetic properties of 
the elements, an important coordinat- 
mg prmciple, known as the exclusion 
principle, was enunciated m 1925, by 
theAustnan-bom, mathematical phys- 
icist W Pauh He based his conclusion 
on experimental observations, and the 
principle has, as yet, no theoretical 
basis Nevertheless, in its most general 
form, expressed m the language of wave 
mechanics, it must represent something 
fundamental in the structure of matter 
Here it mil be adequate to state the ex- 
clusion pnnciple in the special terms 
applicable to the problem of the dis- 
tnbution of the extranuclear electrons, 
thus it is impossible for any two elec- 



103 


The Structure of (he Atom 


irons in the same atom to have their 
four quantum numbers identical. In 
other words, no more than one electron 
can occupy each possible energy state, 
as defined by the four quantum num- 
bers (§ 4.55). 

4.65. This simple idea, in conjunc- 
tion with the rules which give the per- 
mitted values for the quantum num- 
bers n,l^in and s, leads to some inter- 
esting consequences. Consider, first, 
the group for which the principal quan- 
tum number n is 1; the only possible 
values of w, I and s which satisfy the 
conditions given in § 4.51 et seq., as 
well as the exclusion principle, are then 
as follows: 


n 1 1 

I 0 0 

m 0 0 

s -h — 

There can consequently be no more 
than two electrons in the first, (n = 1) 
quantum group. 

4.66. In the second group, with n — 
2, there are eight possibilities, thus: 


?i 22222222 

I 0 0 111111 

7 n 0 0 -1 -1 0 0 +1 +1 

s 4 + 1 + - 


DisTBiEtmoN OF OrbitaIj Electrons 


1 

IN Quantum Groups 

= 01 2 3 4 



Maximum Number of 
Electrons 

Total 

n — 1 

2 _ — — — 

2 

2 

2 6 — — — 

8 

3 

2 6 10 — — 

18 

4 

2 6 10 14 — 

32 

5 

2 6 10 14 18 

50 

2 X3S 

2 X 4^, and 2 X 5^ 

respec- 


lively. The maximum numbers are 
thus proportional to 1^, 2^, 3^, 4^ and 5^. 
This is in general accord with the idea 
that the higher the value of the princi- 
pal quantum niunber n, the more time 
do the electrons spend at an increasing 
distance from the nucleus. The greater 
the distance, the more the space avail- 
able, and hence the larger the number 
of electrons that can be accommodated. 
As an approximation, therefore, the 
principal quantum numbers may be re- 
garded as representing a series of spher- 
ical shells, of increasing radius, about 
the central nucleus. The first can ac- 
commodate a maximum of two elec- 
trons; the second, eight; the third, 
eighteen; and so on. 

The Periodic System and 
THE Orbitae Electrons 


It is seen that in no case are all four 
quantum numbers identical, so that 
there can be up to eight electrons, and 
no more, in tlie second principal quan- 
tum group. Of lhe.se eiglit electrons, 
two have I = 0, and six have 1=1. 

4,67. Working in this manner, the 
results in the accompanjdng table may 
l>o derived for the maximum numbers 
of electrons corresponding to n values 
from 1 to 5, for each of the permissible 
I v.'ducs. Attention may l>e called to 
the {.act that the total maximum num- 
in the successive principal quan- 
tnin (rj) levels are 2, 8, IS, 32 and 50, 
wiich may be written as 2 X 1-, 2 X2^ 


4.68. By means of the results given 
in the foregoing table many of the gen- 
eral features of the periodic system of 
the elements can be interpreted. If, in 
addition, information obtained from 
atomic spectra, from the characteristic 
X-rays and from chemistry is utilized, 
it is possible to deduce the details of 
the arrangement of the extranuclear 
electrons in the atoms of most ele- 
ments. Tlie general procedure is to 
imagine the electrons, equal in number 
to the positive nuclear charge, i.e., to 
the atomic number of the element, to 
be added to the sj'stem one at a time 
until the complete atom is built up. It 



104 


Sourcebook on 
IS then necessary to find m which quan> 
turn level each successive electron la 
accommodated This apparently ardu* 
ous procedure is greatly simplified by 
assuming that the mam inner electron 
grouping of any atom is the same as 
that of the element preceding it m order 
of atomic number All that is required, 
then, IS to determine the position of the 
additional electron which distinguishes 
one element from the next in the peri- 
odic table Thus, starting with hydro- 
gen, which has one electron, its position 
is established as being m the n = 1 . 
level, then with the next element, he- i 
hum, the additional electron completes i 
this group In the third element, lith- 
ium, It IS concluded from its chemical ! 
and spectroscopic properties that the | 
extra electron must enter the second i 
pnncipal (n « 2) quantum level This I 
procedure is continued throughout the 
senes of elements In a feu instances 
the assumption that the inner grouping 
is unchanged from one element to the 
next higher one does not hold, but there 
are definite indications when this is the 
case and due allowance can be made 
4 69 One of the many interesting 
results which has emerged from consid- 
erations of the type just described is 
that the principal quantum levels do 
not fill up with electrons stnctly in the 
order 1, 2, 3, 4 etc IVliene\ er the out- 
ermost group, other than the first, con- 
tains eight electrons, the next electron 
goes into a higher principal quantum 
level, irrespective of uhether any va- 
cant places remain to be filled or not 
The result is the regular repetition of 
properties at definite intervals, as ex- 
emplified by the periodic system, the 
completion of each period, after the 
first, being marked by the presence of 
eight electrons m the highest quantum 
le\ el The number of electrons m the 
various principal quantum levels for 
the elements of Group 0 of the penodic 


Atomic Eiiergy Chap IV 

table, 1 e , the inert gases of the atmos- 
phere (§ 1 47), are sho\vn below It 
will be seen that wth xenon, for exam- 


Arranoement of Electrons 
IN Gbodp 0 Elements 




i = 1 

h' 

h 




FUmenl 

AUjmtc 

Number 

Number of eleclrons 
guanlwoi levels 

in 

lleltum 

1 2 

1 2 , 


_i 





Neon 

1 10 

1 2 , 

8 


' 





Argon 

1 18 

1 2 

8 

8 

— ' 

— 

_ 

Krypton 

i 36 

1 2 

8 

18 

8 

— 



Xenon 

, 54 

2 ' 


18 

181 

8 



K&don 

86 

, 2 1 

8 ! 

18 

52] 

is! 

8 


pie, eight electrons have entered the 
fifth {n s» 5) principal quantum level, 
although there are still fourteen vacan- 
cies m the fourth (n «« 4) level The 
same is true for radon, which contains 
electrons m the sixth (n 6) level, al- 
though the fifth (n « 5) quantum level 
is far from complete 
4 70 Attention must be drawn to a 
number of aspects of the table given 
above First, it will be seen from the 
last line that when completed the first 
four groups contain 2, 8, 18 and 32 elec- 
trons, respectively, as required by the 
exclusion principle Second, the num- 
bers of elements m successive periods 
of the periodic system, which are equal 
to the differences in the atomic num- 
bers of the Group 0 elements, are 2, 8, 
8, 18, 18 and 32 The increase from 8 
to 18, and from 18 to 32, is e\ idently 
accounted for by the possibility of a 
laiger number of electrons entenng the 
higher quantum levels Finally, it will 
be noted that the difference between 18 
and 32 electrons in the fourth (n 4) 
quantum level accounts exactly for the 
kno^vn number of elements m the rare 
earth, or lanthanide, senes (§ 1 48) It 
is not unexpected, therefore, that a 



105 


The Structure of the Atom 


sirnilar group — the actinide series 
should exist beyond radon, as the fifth 
(n = 5) quantum level fills up from 18 
to 32. 

Chabacteristic X-Rays 

4.71. The characteristic X-rays of 
the elements, or X-ray spectra, as they 
are often called, differ in one important 
respect from the ordinary or optical 
spectra considered above. In the for- 
mer case, the wave lengths, or frequen- 
cies, for a particular type of X-ray, 
namely 7v, L, M etc., var}- re^larly 
from one element to the next, with in- 
creasing atomic number, as was first 
shown by Moselej’’ (§ 4.24), and subse- 
quently verified by others. With opti- 
cal spectra, however, there is a peri- 
odicity, analogous to that observed 
with many other physical and chemical 
properties. The reason for this differ- 
ence is that optical spectra are due to 
energy transitions invohdng the outer- 
most electrons, and the arrangement of 
these among tlie quantum levels has a 
periodic character, as just indicated. 
The characteristic X-rays, on the other 
hand, must be caused by transitions of 
another kind. If an atom absorbs a 
sufficiently large amount of energy, 
very much larger than that required 
for the production of optical spectra, 
one or more of the electrons from an 
inner quantum level will be raised to a 
much higher level, or even completelj’’ 
ejected from the atom. The vacancy so 
created will then immediately be filled 
by another electron monng into the 
lower level from one of the upper elec- 
tronic energy le.velsj in doing so an 
X-r.ay line characteri.stic of the element 
'^dll be produced. 

4.72. Calculations show that if the 
initial absorption of encrg\’ results in 
the flection of one of the two electrons 
in the first (i: = 1) princi))al qu.antum 
level, the X-ray prt^uced, ns another 


electron moves into the vacancy, be- 
longs to the K series. For this reason 
the first quantum level is frequently 
referred to as the K level. Similarly, 
X-ray lines in the L series are obtained 
when the absorption of energy by an 
atom causes an electron in the second 
(n = 2) quantum group, also called the 
L level, to be transferred to a higher 
level. Members of the M series result 
from the removal of an electron in the 
third (n = 3) quantum level or M 
level, and so on (Fig. 4.5). 


K SERIES L SERIES U SERIES 


W (» = 0) 


U (n « 3) 


L (n <= 2) 


ir U 


Fig. 4.5. Interpretation of characteristic 
X-rays in terms of energy levels. 


4.73. If any one X-ray series, say the 
K series, is considered, it can be seen 
that in passing from one element to the 
next of higher atomic number, the elec- 
tronic transition responsible for the 
X-ray remains essentially unaffected. 
In each case, an electron from one of 
the higher energj’- levels must move 
into the vacant position in the K level. 
There will, of course, be small differ- 
ences in the energy with increasing 
atomic number, and hence the wave 
lengths, or frequencies, of the charac- 
teristic X-raj's should varjf gradually 
from one element to the next, as is ac- 
tualh' obseiA'cd. 

4.74. The amount of energy required 
to produce a particular characteristic 
X-ray line can be readily calculated by 
means of the Planck quantum theory, 
equation (3.19) or (3.20) being espe- 



106 


Sourcehoot on . 
cially convenient for this purpose One 
of the K lines of the element tun^cn, 
for example, has a wave length of 0 213 
A, I e , 0 213 X 10^ cm Upon inseit- 
mg this figure into equation (3 19), the 
corresponding energy is found to be 
5 82 X 10“* Mev or 58,200 ev Conse- 
quently, at least 58,200 ev of energy 
must be supplied in order to excite this 
particular X-ray line of tungsten Be- 
cause the emission of the lines of the 
K senes must be preceded by the ejec- 
tion of an electron from the innermost 
energy level where the electrons are 
held most tightly, large amounts of 
energy are required As might be ex- 
pected, smaller energies are required to 
excite the L senes, and still less for the 
M series, and so on, since the electrons 
are ejected from levels where they are 
less and less strongly held The wave 
lengths increase accordingly and the 
corresponding X-rays have diminished 
penetrating power, i e , decreasing 
hardness (§ 2 86) * 

4 75 AUention should be called 
here to the fact that the foregoing in- 
terpretation applies only to the charac- 
teristic X-rays of the vanous elements 
As usually produced, by permitting a 
stream of fast-raoving electrons to im- 
pinge on a metal anticathode (§ 2 85), 
the X-rays invariably cover a consid- 
erable range of wave lengths, often in- 
cluding the characteristic rays of the 
metal These continuous X-rays do 
not result from electronic transitions 


Atomic Energy Chap IV 

withm the atom, as described above 
but are due to the slowing down of the 
high speed electrons upon sinking the 
anticathode In accordance ^vlth Max- 
well's electromagnetic theory, the de- 
celeration of a moving electnc charge 
must be accompamed by the emission 
of radiation Such radiation, of which 
the continuous X-rays from an anti- 
cathode are an example, is frequently 
referred to by the German name of 
Bremssirahlung, hterally "braking (or 
slowing down) radiation " As a gen- 
eral rule, the fraction of the kinetic 
energy of the electron converted into 
radiation in this manner increases with 
the energy of the electron and with the 
atomic number of the material in 
which It is slowed down 
4 76 The frequency (or wave 
length) of the radiation is related, by 
means of the Planck equation, to the 
energy lost by the electrons In an 
X-ray tube the electrons ivdl have 
passed through a potential of a thou- 
sand to a million volts, so that their 
energies are 10^ to 10* ev, it can be 
readily calculated that if all the energy 
18 converted mto radiation, the corre- 
sponding wave lengths will be from 10'’ 
to cm , which is the X-ray region 
(Fig 3 4) Since various electrons lose 
different amounts of energy, the X-rays 
produced will cover a range of wave 
lengths, the values calculated above 
tepr^enting the minima for the re- 
I spective electron energies 


PROPERTIES OF THE NUCLEUS 


Nuclear Energy Levels 
4 77. The energy levels considered 
so far have been called electronic en- 
ergy levels since they represent differ- 
ent states of the orbital electrons , there 


are also, however, nuclear energy leiels 
which apply m an analogous manner to 
the states of the particles within the 
nucleus Whereas the details of the 
quantum numbers of the electronic 


• The energies necessary to excite X rays are much greater than those required to pr^uce 
opti^l spectra, since the latter are associated with transitiona between the outermost electronic 
levels 



107 


The Struclnre of the Atom 


states have been worked out with 
considerable completeness, as stated 
above, this is far from being the cfcise 
for the nuclear states. There are good 
reasons for believing that various ex- 
cited states of the nucleus exist (§§ 7.39, 
10.120), with energy values in excess of 
the normal or ground state, but very 
little is known about the quantum 
numbers associated with these States. 
It is reasonably certain that there must 
be such quantum numbers, and that 
something akin to the Pauli exclusion 
principle must apply, but the experi- 
mental facts so far available are totally 
inadequate to provide any definite 
information on these subjects. The 
whole problem constitutes a challenge 
to the nuclear scientist. 

4.78. Transitions between pairs of 
nuclear energi' levels give rise to radia- 
tion, just as with electronic energy 
transitions, but since the energj'’ 
cliangcs involved are considerably 
greater in the former case, the radia- 
tions have a much shorter w^ave length. 
In general, the energy separation of 
nuclear levels is of the order of a mil- 
lion electron volts, and if the energy 
quantum B in equation (3.20) is set 
equal to 1 Mev, the wmve length of the 
corresponding radiation is seen to be 
about 1.2 X cm. Such a wave 
length corresponds to very short 
X-rays, or, what is essentially the 
same thing, to gamma raj’^s.* It wdll be 
seen in Chapter VII that the gamma 
radiation, which often accompanies the 
emission of alpha and beta particles in 
radioactihty, is probably due to the 
trau-sition of an atomic nucleus from a 
higher (excited) energj- level to a lower 
level (|7.80). Determination of the 
wave length of the gamma radiation 
jH'nnits the calculation of the corre- 


sponding energy change, and vice 
versa. 

Nucleae Spin 

4.79. Like electrons, the compo- 
nents of .the nucleus, i.e., the neutrons 
and protons, manifest the property of 
angular momentum, usually called 
"spin.” Consequently, every atomic 
nucleus has a definite spin quantum 
number, which is the resultant of the 
individual spins of its constituent nu- 
cleons. Several methods, some of them 
based on spectroscopic studies and 
others involving the behavior of atoms 
in a magnetic field, have been devised 
for determining nuclear spins, and the 
values are knowm for a number of ele- 
ments. From the results it is apparent 
that, like electrons, individual protons 
and neutrons can have spin quantum 
numbers of and only. The 
combination of the spins of these par- 
ticles in the atomic nucleus means that 
the resultant spin quantum numbers 
may be 0, Yz, 1, Yz, 2 etc., i.e., an odd 
or even number of half integers. As is 
to be expected, nuclei with odd atomic 
Aveight, and hence containing an odd 
number of nucleons, have spin quan- 
tum numbers of Yz, Yz, %, Ji, or %, 
no value higher than % having been 
observed. On the other hand, when the 
atomic weight, and hence the number 
of nucleons, is even, the nuclear spin is 
usually 0 or 1, although larger values 
have been recorded in a very few’ cases. 
In the event that the numbers of pro- 
tons and neutrons are both even, the 
spin is apparently ahvays zero. 

4.80. It may be remarked, in pass- 
ing, that the nuclear spin quantum 
numbers provide one of the arguments 
against the presence of electrons in the 
atomic nucleus. The simple correlation 


fundamcntftl difference Iwtwcen X-r&ya and gamma rav's the latter 

niS radiations emitted by an atomic nuclei ^ 

prwlurcd by electrons outside the nucleus (§ 4.71 ct fc?.). nucleus, a ray's are 



108 


SouTceboof. on Aiomic Energy Chap IV 

between the number of particles m the interesting consequences, among other 
nucleus and the nuclear spin would not things, they play an important role m 
then be possible It wll be seen in due determining the permitted transitions 
course that nuclear spins have some betneen nuclear energy levels. 



Natural 'Rjadioactivity Chapter V 


Early Radioactive 
Measurements 
6.1. In an earlier chapter an ac- 
count was given of the discovery of 
radioactivity, and the alpha, beta and 
gamma rays were described briefly 
Studies of the behavior of alpha par- 

floint ^’^eady seen, to the 

struf>r^'”°"^°? ^ theory of atomic 

identiflcation 

nblr ° r’ 

nalnrp ^i*^ fundamental particles of 
ture. Investigations of the phe- 

liave'^htrf radioactivity 

tlinn fi ®fr'king consequences other 
han lmsc just mentioned. Itis,there- 

oi rndioactwtyin greater detail. 

iiiitiai fbat after his 

u^ al observation of the photographic 

tbal tll p f^'^'^querel found 
cbaLe an "'U'-e able to dis- 

'^'be instru- 

'^nidc and ''ras somewhat 

Sv tw be was able to 

ubirn IS S of ura- 

cmitted fi !• ^ be metal itself, 
uof make a he could 

reintho I :!.‘^^b‘'^blc comparison of the 
t.*rj!jic *ft tJie various ma- 

bon. mI, 'b"^ 'be Polish- 

'v.as then n who 

uetiii nrmr.rf‘ * ®bidymg the mag- 
_ properties of iron and sinni 


RADIOACTI^rE ELEMENTS 


turned her attention in 1898. Her hus- 
and, Pierre Curie, in cooperation with 
his brother, Jacques Curie, had dis- 
covered the property of piezoelectricity* 
whereby certain cr 3 rstals, quartz and 
some salts of tartaric acid in particular 
are able to produce a difference of 
electric potential when subjected to 
pre^ure. Utilizing the fact that the 
electric current generated is propor- 
Lonal to the pressure, applied by 
means of weights, the Curie brothers 
were able to design a relatively simple 
fo™ 0 electrometer tor the 4as“S! 
ment of verj' small currents. 

6.3. It was a piezoelectric device of 

nr^duL . of tto radiations 

Pomds^Th^ ''™” oom- 

• The apparatus consisted of 

two parallel horizontal plates L 

nected through a high-voi&"^ 

to a sensitive galvanometer. The ura 

mum compound was placed on thp 

over plate, so that {he radtoil 

omzed the air between the plates and 

tte caused a small electric char» to 

tude o°f Si '’“ometer. Tl,e mfgni- 
ure of "’•''O'* "’US a meas- 

the / ‘‘.'O Povcr or actmty of 

tl 0 ra* „ deterS^ed 

duSd r™® ‘•'0 olectricity prS 

above. ‘'OStai, as descnbed 


oieel, , aoove. 

^ ^ *■ 


in 



110 Sourcebook on 

6 4 In this manner, Madame Cune 
found that "all the compounds of ura- 
nium studied are active and, in genera), 
the activity is greater the more urar 
nium they contam " She also reported 
that thorium compounds possessed 
BimilaT activity — a discovery made in- 
dependently a few weeks earlier by 
G 0 Scdimidt in Germany — and called 
attention to the fact that the active 
elements, uranium and thorium, are 
among those with the highest atomic 
weights 

Discovery of Polonium 

6 6 While studying the lomzmg 
power of the radiations from various 
uranium minerals, Mane Cune noted 
that two of these minerals namely, 
pitchblende (uranium oxide) and chal- 
colite (copper uranyl phosphate), are 
much more active than uranium itself 
"This fact/ she went on to state, “is 
very remarkable and leads to the bdief 
that these mmerals may contam an ele- 
ment much more active than uranium ” 
At this point, because of the challeng- 
ing nature of the problem, Pierre Cune 
put aside his oivn work, and m 1898 he 
]omed his wife m an attempt to dis- 
cover the cause of the imexpected ac- 
tivity of the mmerals pitchblende and 
'halcolite In a joint publication* they 
■eported “Studies of the compounds of 
uranium and of thorium have shown 
that the property of emitting 
rays, which make the air conductmg 
and which act on photographic plates, 
IS a specific property of uranium and of 
thorium found m all the compounds of 
these metals, being weaker as the pro- 
portion of the active metal m the com- 


Atomic Energy Chap V 

pound IS itself smaller The physical 
state of the substance seems to have an 
altogether secondary importance 
Hence, it appears very probable that 
if certain minerals are more active than 
Uranium and thonum it is because 
they contam a substance more active 
than these metals We have at- 
tempted to isolate this substance m 
pitchblende, and the experiments have 
confirmed the foregoing conclusion 
The pitchblende [used] was about 
two and half times as active [in pro- 
ducmg ionization] as uranium it 
was attacked with acids and the solu 
tion obtamed was treated with hydro- 
gen sulfide The uranium and thonum 
remained in solution, [but] the precipi- 
tated sulfide contamed a very active 
substance, together with lead, bismuth, 
copper, arsemc and antimony " 

6 6 The arsenic and antimony sul- 
fides were dissolved out by means of 
ammonium sulfide, and from the nitric 
acid solution of the residue the lead 
was precipitated as sulfate Ammonia 
W{^ then added to separate the bis- 
muth from the copper t The active 
substance was found to be largely as- 
sociated with the resulting precipitate 
of bismuth hydroxide The separation 
from bismuth proved difficult, but fi 
naJly it was found that if the sulfides 
Were heated to 700*C in an evacuated 
tube, the active sulfide was obtained as 
a black deposit in the cooler regions of 
the tube The Curies then concluded 
“By carrying out these operations 
more and more active products are 
obtained Finally, we obtamed a sub- 
stance whose activity is about 400 
times as great as that of uranium 


• The title of this paper is ' On a new radioactive substance contamed m pitchblende 
and it 13 here that the word radwactiie was used apparent^ for the first time at least in pnnt 
However, in her hfe of Pierre ( 7 «ne, Mane Qine said "To define this new property I 
proposed the term radioactivity ’ The unfdication is that Mane Cune was respomible lor 

t ^e^eader who is famihar with quslitattve inorganic analysis will recognize m this pro- 
cedure the conventional method used lo the ecparstion of metallic cations 



Natural Radioactivity 


We believe, therefore, that the sub- 
stance we have isolated from pitch- 
blende contains a hitherto unkno'wn 
metal ... If the existence of this 
new metal is confirmed, we propose to 
call it polonium, after the name of the 
native country of one of us [Madame 
Curie].” 

Discovery and Isolation 
OF Radium 

6,7. In the course of further investi- 
gation, the Curies, together wth an 
assistant, G. Bdmont, found that pitch- 
blende contained “a second strongly 
radioactive substance, entirely differ- 
ent from the first [i.e., polonium] in its 
chemical properties . . . this new ra- 
dioactive substance . . . has all the 
chemical characteristics of barium. It 
is not precipitated by hydrogen sulfide, 
ammonium sulfide or ammonia; the 
sulfate is insoluble in water and in 
acids, the carbonate is insoluble in 
water; and the chloride is very soluble 
in water but insoluble in concentrated 
hydrochloric acid and in alcohol. . . . 
Although the [product] consists mainly 
of barium, it contains, in addition, a 
new element which confers radioactiv- 
ity on it and which resembles barium 
in its properties. . , , Upon dissolving 
• . . [the mixed] chlorides in water 
and partly precipitating Arith alcohol, 
the precipitated portion is much more 
active tlinn that remaining in solution.” 

6.8. By dissolving the precipitate in 
water and reprecipitating with alcohol, 
end repealing this procedure several 
times, a product was finally obtained 
vdth an actirity 900 times as great as 
that of uranium. It Avas only lack of 
m.'vtcrial, Avhich diminished steadily in 
Ouantity as the barium chloride AV’as 
resnoyod, that prevented even higher 
activities being attained. The results 
Wore explained by the presence of a 

* Prom Osp ]La(in ronsus (ray). 


Ill 

new element to which Avas given the 
name radium* Since the most active 
product still contained a large pro- 
portion of barium it was concluded, 
quite correctly, that the “radioactivity 
of radium must be enormous,” com- 
pared wdth that of uranium. The Auew 
that the highly active chloride did in- 
deed contain a neAV element Avas sup- 
ported by the spectroscopic observa- 
tions reported in an accompanying 
note by M. Demar5ay; he stated that 
the spectrum contained, in addition to 
the barium lines, a line that did not 
correspond Avith that of any other 
known element. 

6.9. In order to confirm their claim 
to have discovered two new elements 
possessing marked radioactive proper- 
ties, the Curies felt it necessary to 
Avork wdth larger quantities of material 
in the hopes that they might thereby 
obtain appreciable amounts of prod- 
ucts of greater purity. Through the 
influence of the Academy of Sciences 
in Vienna and the cooperation of the 
Austrian Government, Avho then oAvned 
the famous St. Joachimsthal mines in 
Bohemia, the Curies secured a ton of 
pitchblende residues from which much 
of the uranium had been extracted. 
From these residues, Avorking in an old 
shed, under the most primitive and 
difficult conditions, they obtained a 
specimen of radium chloride AA'hich 
they succeeded in separating from its 
associated barium chloride by repeated 
fractional crj^stallization. By 1902, 
Madame Clurie reported, one tenth of 
a gram of radium chloride, of sufficient 
purity to be used for the determination 
of the atomic weight of radium, had 
been isolated from the pitchblende 
residues. This accomplishment repre- 
sented the culmination of a supreme 
effort of scientific faith and perseA’er- 
ance. 


112 


Sourcebook on 
Natijiial Eadioelements 
5 10 Following upon the identifi- 
cation of polonium and radium by the 
Curies, another new radioactive ele- 
ment, named adimum, was discovered 
in pitchblende residues by the French 
scientist A Debierne m 1899, and in- 
dependently, some two years later, by 
h Giesel m Germany In 1900, there- 
fore, five different radioactive elements, 
including uranium and thorium, nere 
known By the end of 1904, largely 
owing to the fundamental discoveries 
made by Ernest Rutherford, then m 
Montreal, Canada, in collaboration , 
with the English chemist Frederick | 
Soddy, tnentj efements possessing 
radioactive properties had been de- 
scribed, this number was extended to 
more than thirty by 1912 and at the 
present time over forty radioactive 


^fomic Energy Chap V 

apecies or radioelments, as they are 
now called, of high atomic weight are 
known to exist in nature 
611 In addition, a few of the lighter 
elements, namely, potassium, rubid 
him, samanum, lutetium and rhenium, 
Possess feeble radioactive properties in 
their normal states It should be em 
Phasized that the elements referred to 
here are those which are radioactive in 
theformsm which they occurnaturally 
One of the outstanding achievements 
modem atomic science has been the 
Production of virtually every one of 
the knoTvn elements, and of some 
others previously unknoivn, m radio- 
active fhrms 'Ihis aspect of radioac 
tivity and its important applications 
Ml science and medicine will be de- 
ecnbed m later chapters 


RADIOACTIVE DECAY AND RECOVERY 


URANimi X AKD Thorium X 

6 12 While studying the radioac- 
tive properties of uranium in 1900, 
William Crookes, whose work on cath- 
ode rays was mentioned m Chapter II, 
made a somewhat surprising discovery 
He added ammonium carbonate to a 
solution of uranium nitrate m water 
until the precipitate which first formed 
had almost completely redissolved, 
leaving a small quantity of a flocculent 
residue Upon examining the effect of 
this residue on a photographic plate, he 
found It to be very active, whereas the 
product obtained from evaporating the 
solution, which actually contained es- 
sentially all the uranium, was virtually 
inactive 

5 13 This unexpected result led 
Crookes to suggest that, contrary to 
the views of Becquerel and the Cunes 
radioactivity was not an inherent prop- 
erty of the element uranium, but of an 


extraneous substance associated with 
it To this active substance Crookes 
gave the name uramum X Apparent 
Confirmation of this idea was provided 
by Becquerel himself when he observed 
that if banum chlonde was mixed with 
a solution of a uramum salt and then 
sulfunc acid added, the precipitated 
banum sulfate, which contained none 
of the uramum, earned virtually all of 
the radioactivity 

6 14 However, Becquerel was not 
s^tKfied with Crookes’s suggestion that 
the observed activity of uramum salts 
Was due to an impurity For, he said, 
“the fact that the radioactivity of a 
given salt of uranium, obtained com- 
mercially, 13 the same, irrespective of 
the source of the metal, or of the treat- 
ment it has previously undergone, 
makes the hypothesis not very prob- 
able Since the radioactivity can be 
decreased [by suitable precipitation] it 



Naiural Radioactivity 


113 


must be concluded tbat in time the 
salte of uranium recover their activ- 
ity." Tins conjecture was verified by 
Becqucrcl in 1901, for having prepared 
some uranium salts whose activity had 
been removed in a barium sulfate pre- 
cipitate, he put them aside for eighteen 
months. At the end of that time he 
found that the uranium compounds 
had completely regained their activity, 
as regards their ability to render air 
conducting and to affect a photo- 
graphic plate. The barium sulfate 
precipitate, however, had become com- 
pletely inactive, “The loss of activ- 



TlWE IN days 


Fig. 5.1. Decay of thorium X and re- 
roverj' of thorium, as observed by Ruther- 
ford and Soddy. 

ity," wrote Becquerel, ", . , shows 
that the barium [sulfate] has not re- 
moved the essentially active and per- 
manent part of the uranium. This fact 
constitutes then a strong presumption 
in f.avor of the existence of an activity 
peculiar to uninium, although it is not 
proved that the metal be not inti- 
mately united with another verv active 
prcKiuct." 

5,16. Observations analogous to 
tho*-e tiesorihed abo^'e were reported bv 
Ihitherforcl and Soddy in 1902 as the 
result of experiments with thorium 
compounds. Thorium nitrate was dis- 

_ * Wlu'n Ibuhcrfoni vrns elevated to the I 
irapmr.rii n<le in the history of radioactivity, 


solved in water and sufiicient ammonia 
was added to precipitate the whole of 
the thorium as its hydroxide. The 
filtrate was evaporated to dryness and 
heated to drive off the ammonium 
salts; the small residue remaining, 
Avhich Rutherford and Soddy called 
thorium X, by analogy with Crookes’s 
uranium X, carried essentially aU the 
radioactivity, whereas the thorium hy- 
droxide precipitate Avas inactive. How- 
ever, in the course of a fcAV days, it Avas 
noted that the thorium X was losing 
its activity, Avhile the thorium, AA^hich 
had been freed from thorium X, re- 
covered its actiAuty at the same rate, as 
shown in Fig. 5.1.* 

6.16. Rutherford and Soddy also 
made a quantitative study of the rate 
of decay of the actiAuty of uranium X 
and of the rate of recovery of the 
activity of uranium after the uranium 
X had been removed. The evurves ob- 
tained were similar in shape to those 
in Fig. 5.1, the only difference being 
that it required about six months for 
uranium to regain its original activity, 
although thorium recovered in about a 
month. Since the uranium (or thorium) 
recovers its activity at the same rate 
as the activity of the separated ura- 
nium X (or thorium X) decays, it can 
be tmderstood why, in the ordinary 
Avay, uranium and thorium compounds 
do not e.\hibit any appreciable change 
of activity A\ith time. 

6.17. It AA-as established, therefore, 
that uranium and thorium Avere asso- 
ciated Avith uranium X and thorium X, 
respecth'ely, Avhich differed in their 
chemical and radioactiv'e properties 
from ordinaiy uranium and thorium. 
This fact alone is not in any waj’ un- 
usual, but the point that is remarkable 
is that after being remo\red, the active 
species is regenerated in the cour.se of 

itish pcerapio, this diapram, which played an 
vas incorporated in his escutcheon. 



114 


Sourcehook on Atomic Energy 


about SIX months by the uramum and 
one month by the thorium After re- 
generation m this manner, the uramum 
X and thonum X can again be sepa- 
rated, and the almost inactive residue 
will once more recover its activity m 
due course This removal and recovery 
of the activity can be repeated almost 
indefinitely Before proceeding to con- 
sider the interpretation of these results, 


Chap V 

pamed by the development of an 
"induced” activity in the containing 
vessel or on materials in the immediate 
vicinitv This was later shown by 
Rutherford to be due to what he called 
an active deposit, left by the emanation 
as it decayed 

Theory op Radioactive 
Disintegration 


it IS necessary to describe some other 
observations which have a bearmg on 
the problem 

Radioactive Emanation 
6 18 In 1899, Mane and Pierre 
Cune had reported that substances 
placed in the vicinity of a radium 
preparation acquired an "induced” or 
"excited” activity, and in the same 
year, R B Owens of Columbia Uni- 
versity, working m Rutherford s labo- 
ratory in Montreal, noted that the 
radioactivity of thorium appeared to 
be affected by currents of air An ex- 
planation of these diverse phenomena 
was provided by the work of Ruther- 
ford m 1900 He found that thonum 
salts continuously liberate a radioac- 
tive gas, which he called emanahon, the 
activity of this emanation decays quite 
rapidly, but in doing so it leaves 
an "induced” activity on surrounding 
matter 

519 That radnim salts emit an 
emanation was proved by E Dom in 
1900, and a corresponding actinium 
emanation was discovered in 1903 by 
A Debierne The emanations were 
found to behave like ordinary gases in 
all respects, and were even capable of 
being liquefied at low temperatures 
their radioactivity remaining unaf- 
fected In each case the decay of the 
activity of the emanation was accom- 
* The term ' metabolon ' from the Greek m 
describe a radioactive element, but it was not 
t Uranium X is now known to be a nuxtun 
thi« does not affect the mam argument given 


6 20 With the object of correlating 
th^ perplexmg facts, Rutherford and 
Soddy proposed m 1902 the theory of 
radioactiie disintegralion It was sug- 
gested that the atoms of radioelements, 
unlike those of inactive elements, un- 
dergo spontaneous disintegration with 
the emission of alpha or beta particles 
and the formation of atoms of a new 
element In the words of Rutherford 
and Soddy "The disintegration of the 
atom and the expulsion of a 
charged particle leaves behind a new 
system lighter than before and possess- 
ing physical and chemical properties 
quite different from those of the ongi 
na! parent element The disintegration 
process, once started, proceeds from 
state to stage with measurable veloci- 
ties in each case ”* 

6 21 On the basis of these views the 
observations recorded above find a 
ready explanation Uranium, for ex- 
ample which itself possesses only weak 

activity, m^v be supjiosed to undergo 
disintegration with the formation of 
the much more active uranium X hav- 
ing chemical properties different from 
those of its parent f Upon the addi 
tion of ammonium carbonate, the ura- 
nium X IS precipitated, but the uranium 
IS retained in solution, the liquid is 
consequently inactive while the solid 
residue is highly active 

6 22 In the course of tune the ura- 

Cofiofos, meaning changeable was suggested to 
enersily adopted and it is now obsolete 
resulting from successive disintegrations but 



Naiural Radioaciivity 


nium X ra the precipitate disintegrates 
further, the product being less active; 
hence there is a gradual decay of its 
activity. The disintegration stages 
may thus be represented, approxi- 
mately, by the following scheme: 

Uramum — ^ Uranium X — > Product, 
(feeble (strong (feeble 

activity) acti\dty) activity) 

The uranium in solution, however, con- 
tinues to disintegrate, and in doing so 
produces more uranium X; the activ- 
ity consequently increases until a cer- 
tain equilibrium amount is attained. 
The uranium is then decaying to form 
uranium X just as fast as the latter is 
breaking up; the quantity of uranium 
X present, and hence the observed 
activity, remains essentially constant. 

6.23. It should be mentioned that 
although the product formed by the 
disintegration of uranium X appears to 
be almost inactive, it is actually under- 
going further disintegration. It is now 
known that this process is extremely 
slow, and if the material were kept for 
a .sufficient length of time, probably 
some hundreds of years, it would un- 
doubtedly e.xhibit appreciable radio- 
activity. 

6.24. Tlie three radioactive ema- 
nations, similarly, are to be regarded 
fis disintegration products of radium, 
thorium and actinium, respectively. 
Tlie fact that the^*’ are gases is imma- 
terial, since the physical and chemical 
properties are not necessarilj'- related 
to those of the parent elements. In a 
relatively short period, the emanations 
themseU'cs disintegrate; the products 
am solids and so they are deposited on 
wuTounding materials, thus causing 
me "induced’' acti\'ity first obsenmd 

tiie Curios. These products also 
rtmniegnae in ixim until, ultimately, 
00 inactive end product is formed. 


115 

6.26. Becquerel, Pierre Curie and 
others had found that radioactive 
changes could not be affected by high 
or low temperatures, or by any other 
available physical means. The rates 
of ordinary chemical changes, on the 
other hand, are markedly influenced 
by changes of temperature, and some- 
times by pressure. The implication of 
this difference between radioactive and 
chemical processes was realized by 
Eutherford and Soddy who wrote: 
“Since . . . radioactivity ... is an 
atomic phenomenon . . . in which new 
types of matter are produced, these 
changes must be occurring within the 
atom. The results that have so far 
been obtained, which indicate that the 
velocity of the [radioactive] reaction is 
unaffected by the conditions, make it 
clear that the changes in question are 
different in character from any that 
have been before dealt with in chem- 
istry. . . . Radioactivity may there- 
fore be considered as a manifestation 
of subatomic change.” 

6.26. Although the theory of the 
spontaneous disintegration of radio- 
active substances is now accepted 
without reserve, it caused consterna- 
tion in the realms of science during the 
early years of the present century. In 
spite of its undoubted ability to ac- 
count for the facts of radioactivity, 
many chemists and phj’^sicists ex- 
pressed strong opposition to the theory, 
because they felt that it was contrary 
to the established views on the per- 
manence of the atom. 

6.27. However, in the course of time 
it became evident that radioelements 
were in fact unstable, and that the 
atoms were undergoing spontaneous 
change at a finite rate. The disinte- 
gration theorj', as proposed by Ruth- 
erford and Soddy, consequently forms 
the basis for the interpretation of the 
properties of the forty or so natu- 



120 


Nx _ ^ _ 
Nb Xa 


Sourcebook on Atomic Energy 
at (6 8) 


Since Xx and Xb are both constants the 
quantity Xb/Xa is also a constant, and 
hence the ratio of the amounts of any 
t\\ 0 members of a disintegration senes 
wll be constant m the condition of 
radioactive equilibrium 
6 44 The results just derived have 
some interesting and useful appli- 
cations In 1903 Rutherford and 
Soddy made the suggestion that ra- 
dium ivas itself a disintegration prod- 
uct of another element, and m 1904 
j^cnAhnahirf AVin? snicu findmir 

Tvas always found in uranium minerals, 
It might be a descendant of uranium 
He stated that, if this ^\ere so, the 
ratio of uranium to radium m these 
minerals should be constant, os re- 
quired by equation (5 8) Shortly 
thereafter, B B Boltwood, of Yale 
Umversity, H N McCoy, of the Uni- 
versity of Chicago,* and R J Strutt 
(see § 2 99), independently, reported 
that this was m fact the case, bo that , 
radium and uranium were proved to be 
members of the same disintegration 
senes As far as is known, all uranium 
minerals contain 1 part of radium to 
2 8 million parts of uranium 
6 46 If uranium is an ancestor (or 
precursor) of radium, then, upon keep- 
ing a pure specimen of uramum for ! 
some time, radium should gradually 
accumulate An attempt to test this 
possibility was made by Soddy in 1905, ! 
but the results were unsatisfactory ; 
because of an impurity in the uranium i 
However, in 1907, Boltwood showed | 
that an element, which he called ' 
tonti^OT, that decayed very slowly, lay ! 
between uranium and radium Conse- j 
quently it would take many years to ! 


Chaj) V 

Produce a detectable amount of the 
fatter from the former, unless very 
Wge quantities were used 

The Half Life op a 
Radioelement 

6 46 As an alternative to the radio- 
^tive decay constant, another con 
^tant, introduced by Rutherford in 
I 1904 called the half life, is commonlj 
j <imployed as a characteristic property 
I <if a radioelement The half life is the 
time required for the radioactivity of 
^ given amount of the element to decay 
to half its initial value This tune 
' ^egxseaied bs' dee ssmbel r, esa de 
^cadily evaluated from equation (54) 
the following manner After the 
^hpse of time T, the number of radio- 
hctivo atoms AT, voll be half the initial 
*\umberf^o sothatiVf/iVoisH Upon 
‘hserting this value for Nt/Na in cqua 
tion (6 4), and replacing t by the half 
^Ife T, It IS seen that 

logH “ -D4343Xr 
hr 

log 2 = 0 4343Xr 
Since log 2 13 0 3010, it follows that 

77 _ 0093, (59) 

X 

find consequently if the decay constant 
X IS known, the half life of the radio- 
Element, which is equally definite and 
specific, can be calcidated very simply 
5 47 The fact that radioactive ele- 
bleats disintegrate in an exponential 
^banner has some cunous consequences 
Suppose, for the sake of illustration 
f-hat a particular radioelement has a 
half hfe r of 1 hour Starting forct 
®mple, with 1 gram of the element, one 


•B B Boltwood and H N McCoy pioneer^ the study of radioactivity m the 

States McCoy 3 active interest in this fidd ext^ided from 1903 up to the wartime atom*- 
energy project lU 1942 



Natural Radioadmty 


half, i.e., 0.5 gram, will have disinte- 
grated by the end of 1 hour, so that 0.5 
gram remains. During the next hour 
one-half of this amount, i.e., 0.25 gram, 
will disintegrate, leaving 0.25 gram. 
By the end of the third hour, another 
0,125 gram will have decayed, and so 
on. In each successive hour the actual 
amount which disintegrates is less than 
in the preceding hour, although it is 
always the same fraction of the amount 
present at the beginning at that par- 



ticular hour (Fig. 5.2). In general, 
since the activity is reduced to one 
half of its initial value in the time T, 
the fraction remaining after n such 
inten'als, i.e., after time nT, A\dU be 
(1^)". Although this fraction may be- 
come Very small, it can, theoreticallj’^, 
never fall to zero. However, after ten 
times the half life the activity has 
fallen to (H)'®, which is about 0.001, 
or 0.1 per cent, of the original amount, 
So that the remaining activity is negli- 
gible in comparison with the initial 
value. 

, combining equation (5.S) 

uiUi (u.O) so as to eliminate the X’s, it 
5' sound that in the state of radioactive 
equshludum 

-Vb constant. (5.10) 


121 

Hence, if the ratio of the equilibrium 
amounts of two elements in a par- 
ticular series can be determined, and 
the half life of one of them is known, 
the half life of the other can be calcu- 
lated. It will be shown below (§ 5.51), 
that for elements which disintegrate 
moderately rapidly, the half lives can 
be found by direct observation of the 
rate of decay; but w^hen the disinte- 
gration is very slow, and the half lives 
are very long, direct measurements are 
not too accurate. In cases of this kind 
use may be made of equation (5.10). 
For example, uranium minerals, most 
of which are old enough for radioactive 
equilibrium to have been established, 
contain 1 atom of radium to every 
2.8 X lO*^ atoms of uranium, so that if 
the latter is taken to represent A and 
the former B, the value of Na/Nb at 
equilibrium is 2.8 X 10°. The half life 
Tb of radium is knoum from direct 
measurements to be 1620 years, so 
that the half life Ta of uranium is 
given by equation (5.10) as 

Ta = ~ Tb = 2.8 X lO® X 1620 

A B 

= 4.5 X 10'’ years. 

This is the accepted value for the half 
life of the common form of uranium. 

6.49. In view of the fact that radio- 
elements are undergoing continuous 
disintegration, it may be wondered 
that any of these species still exist. 
The explanation is that each natural 
radioactive series has a precursor of 
verj^ long half life. As seen from the 
calculation made above, the half life 
of uranium is 4.5 })illion years, com- 
pared with an estimated 2.5 billion 
years for the age of the earth. This 
means th.at more than two thirds of 
the uranium present when the earth 
was formed still sundves. Hence, as 



122 


SouTcehook on Aiomtc Energy Chap V 


the various radioactive products de- 
cay, they are replaced by the disinte- 
gration of their parents, the supply 
being maintained by the vast reserve 
of uranium It is of interest to note 
that only three series of radioelements 
exist m nature, namely, the uranium, 
thorium and actinium senes (§ 5 56) 
although four should be possible It 
will be seen later (§ 5 65) that the 
longest-hvcd member of the fourth 
senes has a half life of about 2 million 
years, so that in the time which has 
elapsed since the earth nas formed it 
has decayed almost completely 

DETEBM1NA.TION OF THE DeCAY 

Constants and Half Lives 

6 60. As already implied the deter- 
mination of the radioactive decay con- 
stant, and consequently of the half life, 
13 one of the most significant measure- 
ments made •with a radioelement The 
methods employed depend on the as- 
sumption, which IS m complete accord 
with all the knoism facts, that each 
radioactive atom of a given species 
expels from its nucleus either one alpha 
or one beta particle upon disintegra- 
tion * As a result the number of atoms 
disintegrating in a given time, and 
hence the rate of disintegration, could 
be evaluated by counting the number 
of alpha or beta particles emitted The 
co.imtir^ of such ^narticles is an ex- 
tremely important aspect of radioactive 
studies, and several instruments have 
been devised for the purpose These 
will be described m Chapter VI In the 
meantime, some indication will be 
given of the methods of calculation 
usually employed 

6 61 For half lives that are neither 
too long nor too short, say of the order 
of a fraction of a second to several 


months, use may be made of equation 
(5 5) The rate at which particles are 
emitted m a small time interval may 
be taken as proportional to the number 
N of active atoms remaining at that 
instant, m accordance inth equation 
(5 1) If this rate, which can usually be 
determined by automatic counting in- 
struments, measured after time t, is 
represented by It then equation (5 5) 
may be ^vntten as 

log It = log Jfl - 0 4343W, (6 11) 

where Its, which does not need to be 
known, is the disintegration rate at the 
arbitrary zero time By plotting sev- 
eral values of the logarithm of I, 



Flo 5 3 Graphical determination of ra 
dioactive constants 


determined after various time intervals 
ajramst the time, as m Fi^ 53, i 
strai^t bne ^vlll result From the slope 
of this bne it is a simple matter to 
calculate the decay constant X and 
the half life T In the particular 
case shown, for example, the slope is 
—0 0517, wth the time expressed in 
minutes, hence X, which is equal to the 
slope divided by —O 4343 is 0 110 re- 
ciprocal minutes, and the half life, by 
equation (5 9), is 5 82 mmutes The 


• When the phenomenon known as '‘internal conversion'* occurs (§ 7 84), an orbiUd electron 
IS expelled m Edition 




Natural Radioactivity 


average life, i.e., 1/X, is 8.40 minute-s. 

6.62. If the radioactive substance is 
not pure, but consists of two or more 
elements with different half lives, the 
])lot of log It against i is not a straight 
line, but rather a combination of such 
lines, with different slopes, merging 
into one another and forming a curve. 
By analyzing this cun^e it is frequently 
possible to determine the X’s for all the 
radioelemcnts present. If two of these 
species should have verj' closely similar 
lialf lives, then such an analysis is not 
possible. Another circumstance which 
can arise is that the disintegration 
product of an element may contribute 
some activity, and thus confuse the 
results. In this event, the decaj’’ con- 
stant of the parent can be obtained 
from measurements made in the early 
stages, before perceptible amounts of 
the (laughter element have accumu- 
lated. By the use of mathematical 
methods, it is possible to derive the 
decay constants of both parent and 
daughter. 

6.53. ■\^nien the radioelement has a 
moderately long life, the procedure 
de.scribcd above is not satisfactory, be- 
cause the values of It change very 
slowly with time, and it might be 
necessary to continue the measure- 
ments over several ye.ars to obtain 
sufficient, data to make a plot such as 
that in Fig. 5.3. In cases of this kind, 
absolute measurements must be made. 
In the preceding method, it is not 
necessary to know how much material 
is used in the experiment, or the actual 
disintegmtion rate; all that is required 
IS that the same sample remain in the 
same position relative to the counter 
''rlvile the measurements arc Ireing 
made. In the absolute method, the 
•wtual tot .al number of particles emitted 
5n a given time from a definite weight 
m the radioelcment must be known. 


123 

Such measurements are possible, al- 
though not very simple, and they have 
been made in a niunber of cases. 

6,64. If is the number of atoms 
disintegrating, i.e., the measured num- 
ber of alpha or beta particles emitted 
in a definite time interval At, say an 
hour or a day, which is appreciable 
although short in comparison vdth the 
half life of the radioelement, then the 
ratio AN /At may be taken as a good 
approximation to the instantaneous 
rate of disintegration dN/dt. It fol- 
lows, therefore, from equation (6.1) 
that 

X = (5.12) 

^ N 

The radioactive decay constant can 
thus be evaluated by dividing the 
measured quantity AN /At by the ac- 
tual number N of atoms of the radio- 
element present in the sample used 
for the experiments. This number can 
be determined, of course, from the 
knorni weight of the element used in 
the experiment, its atomic weight, and 
the Avogadro number, as described in 
§ 1.63. 

6.66. For radioelements of extremely 
short or extremely long lives, accurate 
measurements of the decay rates are 
difficult to make. In some cases the 
half life may be derived from the ratio 
of the amounts of two elements present 
in radioactive equilibrium, as described 
earliei- in connection with radium and 
uranium (§ o.4S). In other instances 
use may be made of certain equations 
relating tlie radioactive decay con- 
stant, or the half life, to the energy of 
the particles emitted by the particular 
element. These relationships, which 
Avill be given later (§§ 7.24, 7.64), are 
not exact, but thej’’ are sometimes 
useful, especially for disintegrations in 
which alpha particles are produced. 



124 


Sourc^ooh on Atomic Energy 


Chap V 


THE RADIOACTIVE SERIES 


Radioactive Disintegration 
Series 

6 66 As stated earlier, some forty 
species -vvith different radioactive prop- 
erties have been identified as occurring 
in nature By making physical or 
chemical separations when possible, 
as described m § 6 29, by studying 
radioactive decay and growth curves, 
by determining the specific properties 
of the emitted radiations, and m other 
wajs, it has been found that the 
naturally occurring radioelcments of 
high atomic weight, at the end of the 
periodic system, fall into three distinct 
senes These are known as the thonum 
scn.es, the wramum senes, and the 
actinium senes, respectively In the 
first two cases^ the senes are named 
after the longest-lived precursors, tho- 
num and uranium, with half hves of 
1 39 X 10'° and 4 5 X 10° years, re- 
spectuely The parents of these ele- 
ments undoubtedly had shorter lives, 
and consequently no longer exist m any 
detectable amounts The parent of the 
actinium senes is not, as was onginally 
supposed, the element actinium, the 
first member of the senes to be dis- 
covered but rather a much longer lived 
element, sometimes referred to as 
actinouranium,* with a half life of 
7 1 X 10* years 

6 67 Since an alpha particle is iden- 
tical with a hehura nucleus (§ 4 30), it 
has a mass, on the atomic weight scale, 
of 4, to the nearest integer Conse- 
quently, it 13 evident that in any dis- 
integration stage in which an alpha 
particle is emitted, the atomic weig^it 
of the daughter element must be four 
units less than that of the parent On 


the other hand, a beta particle is an 
electron, the mass of which is negligible 
on the atomic weight scale Hence, 
when there is a disintegration accom- 
panied by the emission of a beta par- 
ticle, the parent and daughter elements 
have virtually thesame atomic weights 
From actual determinations m certain 
cases, such as uranium, thonum, ra- 
dium, etc , and by allowing for the 
change accompanying alpha decay, the 
atomic weights of all the known nat- 
urally occurnng radioeleraents can be 
inferred 

6 68 In the accompanying tables 
there are recorded details of the tho- 
num, uranium and actinium senes, 
including the nature of the radiations, 
and the half hves of the respective 
members In addition to the somewhat 
unsystematic names given to the van- 
ous elements as they were discovered, 
but sow becoming obsolete, each is 
associated in the table with the name 
of a familiar element, for example, 
thorium B, uranium B and actmmm B 
inth lead, thonum C, radium C and 
actinium C with bismuth, and so on 
The reason for this correspondence and 
its significance ^vlli be explained m 
Chapter VIII 

6 69 The number given as a super- 
scnpt to the symbol of each element is 
the atomic weight or, more correctly, 
the mass number (§ 8 68) of the radio- 
active species It will be evident in due 
course that the combined symbol, 
given m the third column, is more 
systematic and more informative than 
the older mode of representation 

6 60 Attention may be called to the 
branched disintegration which occurs 


• This IS another name for uranium 235, th® Itty material for the utilization of atoimc 
energy (Chapter XIV) 



Naftiral Radioaciivity 


tu-icc, al least, In each series. Certain 
elements, snch as thorium C, disinte- 
grate in two ways, but with the same 
half life; one mode is accompanied bj-- 
the emission of an alpha particle and 
the other by a beta particle. The two 


125 

types of disintegration always occur 
in a definite proportion in any given 
case; thus 65 per cent of the thorium C 
atoms give off alpha particles to form 
thorium C', while the other 35 per cent 
emit beta particles and become con- 


The Uranium Series 


Radioclcmcrit 


Umiiium I 

1 

Uranium Xi 
1 

Uranium Xj* 

I 

Uranium 11 

1 

Ionium 

i 

Hndium 

i 

Ra Emanation 

1 

Radium A 


1 0.04% 


i 

Radium B 

Astatinc-2i8 


1 

Radium C 

99.r-f)% I 0.049o 

7 ■ 

Radium C' 

Radium C" 


1 

Radium D 


! 

Radium E 


~500%!~io-n:; 

• — ’ 

Radium F 

TIm!tiurn-200 


Radium Ct 
(Und Rrodiirt) 


Conesponding 

Element 

Symbol 

Radiation 

Half Life 

Uranium 

U«8 

a 

4.5 X lO'o yr. 

Thorium 

Th“' 

)3 

24.1 days 

Protactinium 

Pa-’* 

(S 

1.14 min. 

Uranium 

UM4 

« 

2.35 X 10= yr. 

Tliorium 

ThiM 

a 

S.O X 10< yr. 

Radium 

Ra'5« 

ct 

1.62 X 10’ yr. 

Radon 

Rn’« 

a 

3.82 days 

Polonium 

p„n9 

a and /3 

3.05 min. 

Ix'ad 

Pb«* 

§ 

26.8 min. 

Astatine 

AU'» 

a 

2 sec. 

Bismuth 

Bi«‘ 

P and a 

19.7 min. 

Polonium 

Posu 

a 

1.5 X 10~< sec. 

Thallium 

'J'JllQ 

p 

1.32 min. 

Lead 

Pijtio 

p 

22 yr. 

Bismuth 

ppio 

P and a 

5.0 days 

Polonium 

J>Oll0 

a 

140 daj's 

Thallium 

T]i« 

p 

4.23 min. 

Ix'ad 


Stable 

— 


transition (§ 10.123) to form uranium Z the latter has a half iifr. 

>' . )<r.. emittint; P radiation and forming Uranium II ‘ ^ ‘ 






128 


SourcelooK on Alomte Energy 


for the present it be sufficient to 
tabulate the results The name ncp~ 
tunxum senes has been proposed for 
this senes of elements whose atomic 
weights arc represented bj the formula 
4n + 1, because neptunium ra the 
member having the longest life 

6 64 Like the naturally occurnng 
radioactive senes, the neptunium series 
exhibits branched disintegration near 
the end, but it differs m the respect 
that it contains no gaseous emanation * 
Further, the stable end product of the 
neptunium senes is seen to be ordmarj 
bismuth of atomic weight 209, whereas 


Chap V 

in the thorium, uranium and actinium 
senes the nonradioactn e end products 
are nil forms of the element lead 
5 65 The half life of neptumum 
(Np“), the longest li\ed member of. 
the 4n -f 1 senes, is seen to be 2 20 X 
10* years Assuming as is very prob- 
able, that this element existed when 
the earth was first formed, about 
25 X 10® years ago, then the pro- 
portion now remaining can be calcu- 
lat-ed by means of equation (5 4), using 
equation (5 9) to reUte the decay con- 
stant X to the known half life In this 
manner it is found that unless Np*” 


The NErroxicrw Seiues 


Eletnenl 

Sj/tnW 

/ttuhation 

Half Life 

riutoiuum 

i 

Americium 

1 

■Neptunium 

Pu*« 

e 

<--'10 JT 

Am*M 


500 yr 

I Np» 

<* 

220X10‘yr 

* 

Protactinium 

Pa«‘ 

0 

27 4 days 

« 

Uranium 

1 

Thorium 

1 

Radium 

i 

Actinium 

i 

Francium 

i 

Astatine 

i 1 

Bismuth ! 

96% 1 4% 

u*» 

« 

1 62 X 10* yr 

Th«» 

« 

7 0 X 10* yr 

Ra*=* 

0 

14 S days 

Ac» 

a 

10 0 days 

Fr»» 

a 

4 8 xnm 

At*« * 

» 

1 8 X 10-* sec 

Bjtw ! 

0 and a 

47 imn 

i 1 1 

Polonium 

PoW» 

a 1 

4 2 X sec 

1 Thallium ' 

1 t 

Tl*» 

0 

2 2 nun 

i 

Lead 

Pbw ' 

0 

33hr 

Bismuth 
(End Product) 

ni»» 

Stable 

— 


• A collateral branch of the neptunium senes does contain an emanation (Rn*”) as a tnem 
ber(§15 8S) 



Natural Radioactivity 


has a long-lived, but hitherto un- 
known, precursor, the amounts still 
present in nature must be so infinitesi- 
mally small as to be beyond the possi- 
bility of detection. The existence of a 
precursor of higher atomic weight and 
much longer life is highly improbable, 
and hence it can be readily understood 


129 

why the elements of the neptunium 
(4n. -j- 1) series do not occur naturally. 
Even if they did exist at one time, as 
they may well have done, all the mem- 
bers of this series have long since 
decayed virtually to completion, the 
final product being the nonradioactive 
element bismuth. 



IS/leasurement of 'Radioactivity 

Chapter VI 


MEASUREMENT OP RADIATION BY IONIZATION 


Specific Ionization 
6 1. The procedure most v, idely em- 
ployed for the quantitative study of 
alpha and beta particles, and also of 
gamma ray photons, is based on Bec- 
querel’s discovery (§ 2 94) that gases 
become electrical conductors that is to 
say, they are ionized, as the result of 
exposure to radiations from radio- 
active substances As seen m § 5 3, this 
fact was utilized by Madame Cune m 
her comparison of ^e radioactivities of 
vanous materials containing uranium 
The fundamental pnnciples were in- 
vestigated in J J Thomson’s labo- 
ratory in Cambridge, England, by J S 
Townsend m the closing years of the 
nineteenth century, but it is only in 
relati\ ely recent times that they have 
been utilized m a wde variety of 
counters and detectors of radiations 
6 2 Since there is a strong electnc 
6eld m its immediate neighborhood, a 
rapidly movmg charged particle, such 
^ an alpha or beta particle,* has the 
abiUty to eject orbital electrons from 
the atoms or molecules of a gas throng 
which it passes, thus converting them 
into positive ions The expelled elec- 
trons usually remain free for some 
time, although a few may attach them- 
seh cs to other atoms or molecules to 


form negative ions Thus, the passage 
of a charged particle through a gas re- 
sults m the formation of a number of 
lon-pairs (§ 4 31) 

6 3. The intensity of the ionization 
produced by a movmg, charged par 
tide in Its path through a gas is ex- 
pressed by the specific lomzation, this is 
the number of lon-pairs formed per 
centimeter of path For particles of 
the same mass the specific ionization 
increases with the magnitude of the 
charge, and for particles of the same 
energy it increases with the mass, that 
is, with decreasing speed The more 
slowlj moling particle spends more 
time in the vicinity of an atom or 
molecule of the gas through which it 
passes, and so the chances of ionization 
occurnng are thereby increased 

6 4 Alpha particles from radioac- 
tive sources produce 50,000 to 100 000 
lon-pairs per cm of ordinary air, w'hile 
beta particles of similar energy, having 
a hi^er speed and smaller charge, 
would leave no more than a few hun- 
dred ion pairs per cm However, since 
the total path of the beta particle 
would be of the order of a hundred 
times that of the alpha particle, the 
difference in total ionization would not 
be very great Actually, the total nura- 


• The term beta particle includes boUi positive and negative electrons 

130 



131 


Measurement of Radioacliviiy 


])cr of ioii-pairs produced by a charged 
pnrticle is detemined largely by Us 
energy, since an approximately con- 
stant amount is lost for each ion-pair 
formed. For air at standard tempera- 
ture and pressure the formation of a 
single ion-pair requires the expenditure 
of about 32.5 electron volts (§ 3.81) of 
energy by the moring charged particle. 

6.6. Gamma rays and similar elec- 
tromagnetic radiations, e.g., X-raj^s, 
are also capable of ionizing gases. 
They do so indirectly, however, by 
ejecting electrons ^Yith appreciable ve- 
locity from atoms or molecules jjresent 
in the gas or in other substances sub- 
jected to the radiations. It is these 
rapidly moving, sccondarj'' electrons 
which jwoduce ion-pairs in their paths. 
The .s])ecific ionization of the gamma 
radiation thus depends on the energy 
of the expelled electron. 

BmiAVion of Ion-Paihs in 
Electric FiEims 

6.6. Quantitative mcasvircments of 
radioactivity are ba.sed on the counting 
of individual particles, as well as on the 
(lolennination of the total radiation 
received in a given interval of time. 
For these purposes, instrumont.s have 
been developed in which the positive 
and negative ions formed by the ioniz- 
ing radiations are driven toward the 
collecting electrodes by means of an 



Fio. {)A. Dinenimmatic representation of 
apparatu'; u>(hI to study behavior of ion- 
pain-'. 


applied potential under various con- 
ditions. In order to understand the 
behavior of the ions in these circum- 
stances, it is convenient to consider an 
apparatus consisting of a vessel, con- 
taining a gas, air for example, in which 
are fixed tavo parallel metal plates to 
act as electrodes, as shov.Tr at A in 
Fig. 6.1. The electrodes are connected 
to a battery B, so that the voltage can 
be increa.sed steadily from zero to high 
values, and also to an instrument C 
capable of measuring electric current. 

6,7. Normally, the air in the vessel 
does not conduct electricity,* and no 
current will be observed in the instru- 
ment C until the voltage becomes high 
enough — several thousand volts — to 
permit a spark to pass between the 
electrodes. Suppose now a single alpha 
or beta particle, or, in fact, any ioniz- 
ing radiation, is permitted to enter the 
vessel A, wliile a small potential is 
applied to the plates by the battery B. 
A number of ion-pairs will be pro- 
duced, and the applied potential will 
cause the positive ions to travel toward 
one electrode, while the negative ions 
(or elect.rons) move toward the other 
electrode. As a result, charges will 
collect on the electrodes, and the in- 
strument C vtII indicate a pulse of 
current. If the magnitude of this pulse. 



* Cosmic rnys {Cbr.pU'T XVII) and other o\tmneous radiations csu-sc some ionization the 
fiiecl of v.'inch is neglected hero. ’ 




132 Sourcehooh on Atomic Energy Chap VI 

for various values of the applied po- respective electrodes, vath the result 
tential, increasing from zero to several that there will be ample time for many 
thousand volts, is plotted against the of the oppositely charged species to 
corresponding potential, a curve of the recombine, i e , to meet and neutralize 
type represented in Fig 6 2 is ob- one another The size of the pulse 
tamed It may be mentioned that th» registered will consequently be less 
diagram is not drawn to scale, for its than if all the lon-pairs ongmally 
purpose IS merely to indicate the gen- formed succeeded m reaching the elec- 
eral qualitative nature of the variation trodes As the voltage between the 
of the pulse size with the potential plates is increased, the ions travel 
apphed to the plates faster, so that the number of recom- 

6 8. An examination of Fig 6 2 bioations is diminished and the pulse 
show’s that the curve can be divided size is increased Ultimately a point is 
into SIX more or less distinct regions, reached, at the beginning of region II, 
marked I to VI Three of these re- when the ions move to the electrode so 
gions, namely 11, III and V are made rapidly that virtually every ion pro- 
use of in vanous types of instruments duced by the alpha or beta particle 
for the me^urement of radioactivity reaches the electrodes Since a further 
In region I the size of the electrical mcrease m the potential cannot cause 
pulse produced by a single alpha or any increase m the number of lon- 
beta particle increases with the apphed pairs, the pulse size remains unchanged 
voltage, but It attains a constant viUue throughout region 11 The actual volt- 
m region II when it becomes mde- age range over which the pulse size is 
dependent of the voltage The ex- constant depends on many factors, 
planation of these facts is somewhat as such as the nature and pressure of the 
follows gas, the spacing and shape of the elec- 

6 9 When the applied potential is trodes, and so on, but it is roughly 
small, the ions move slowly toward the between 100 and 500 volts 

IONIZATION INSTRUMENTS 

The Ionization Chamber 
6 10 The conditions existing m re- 
gion II are those which are employed 
in the ionization chamber method for 
the measurement of alpha and beta 
particles and also of gamma and 
X-rays Simple forms of the ionization 
chamber method were employed by 
Madame Curie (1898) and b} Ruther- 
ford (1900) m some of the earliest 
quantitative studies of radioactivity 
(Chapter V) The chamber itself is 
made of metal and the electrodes, 
which are insulated from the walls may 
be parallel (Fig 6 I) Alternatively, a 
cylmdneal chamber, the walls of which 


act as one electrode, may be used to- 
gether with a thm metal rod as the 
other efecfrorfe, as m fig d 3 Ihe 



Fig 6 3 Simple type of ionization 
chamber 


nature of the gas m the chamber 
depends on the particular purpose in- 
tended for the instrument, it may be 
air, carbon dioxide, nitrogen, argon or 



Meoisuremcnt of Radioactivity 


methane, among others. The battery 
voltage is adjusted so that the con- 
ditions correspond approximately to 
the middle of region II; a small change 
in the voltage will then not affect the 
pulse size. It is for this reason that 
ionization chambers are operated in 
region II. The charge acquired by the 
electrodes, as a result of collecting ions 
produced by the radiations, is then 
measured by means of a suitable in- 
sti-ument, the nature of which depends 
on the type of radiation being studied. 

6.11. Each alpha or beta particle 
entering the ionization chamber should 
produce a pulse of charge which might 
in principle be counted. However, as 
the specific ionization of a beta particle 
is very small, the pulse is usually too 
feeble to be of practical value. For 
alpha particles, on the other hand, the 
pulses are strong enough to be am- 
plified and counted. Since these par- 
ticles have a short range, rarely more 
than a few centimeters in air, the 
ionization chamber should be small, 
so that the influence of beta particles 
and gamma rays is negligible. 

6.12. The method under consider- 
ation is thus especially useful for 
counting alpha particles in the pres- 
ence of other radiations. For this pur- 
pose a parallel-plate chamber (Fig. 6.1) 
is employed, the electrodes being about 
1 cm. apart. The substance under ex- 
amination can then be placed on the 
lower plate, inside the chamber. If it 
is more convenient to place the active 
material outside the chamber, the 
alpha particles are allowed to enter 
through a "window" consisting of a 
very thin sheet of mica, nylon or 
pliofilm. 

6.13. Tlie response of a shallow ion- 
ization chamber is usually so rapid that 
alpha particles coming at intervals as 
short as 10~^ second or less can be 
detected. Tlio pulses are amplified by 


133 

means of a vacuum-tube (linear) am- 
plifier, and are then either transnaitted 
to an oscilloscope and photographed 
on a moving film, or, more frequently, 
they are recorded by a mechanical 
counter. Wlien the rate of arrival of 
pulses e.xceeds the maximum rate of 
response of the counter, which is about 
30 to 50 per second, an electronic 
device called a scaler is included in the 
measuring system, A common form 
permits one pulse in everj"^ 2, 4, 8 or 16 
etc., to be recorded on the counter. A 
scale of one in 64 is quite common, but 
instruments with much higher scaling 
factors are often used. Scalers based 
on a factor of 10 have also been con- 
structed. The number of pulses indi- 
cated on the counter, multiplied by the 
appropriate factor of the scaler, gives 
the number of alpha particles entering 
the space between the electrodes in the 
ionization chamber. Instead of count- 
ing the total number of pulses, vacuum- 
tube circuits can be used to record the 
rate at which they are received, i.e., 
the number of pulses arriving in a 
specified short time interval. The data 
obtained with a couniing-raie meter of 
this type can be employed directly in 
the determination of half lives. 

6.14. One of the most remarkable 
instruments used in conjunction with 
an ionization chamber and linear am- 
plifier for alpha-particle counting is the 
puhe analyzer, sometimes familiarly 
known as a kicksorter. It consists of 
a number of electronic circuits per- 
mitting only the passage of pulses ex- 
ceeding a certain minimum, those 
rejected being due to beta particles, 
gamma rays and other extraneous ra- 
diations, and then sorting and counting 
them according to size. In this way, 
the alpha particles originating from 
several radioelements in a mixture can 
be counted independently and simul- 
taneously. 



134 


Sourcebook on Aiomic Energy Chap VI 


6 15 For the measurement of beta 
and gamma radiations the ionization 
chamber is modified so that it deter- 
mines the total ionization produced, 
rather than the number of indmdujj 
particles Two main forms of tlie 
instrument ha\ e been used in this con- 
nection and measurements can be 
made i\ith alpha, as iiell as iMth 
beta and gamma rays In the elec- 
trostatic form, of which the gold- 
leaf electroscope used by Becquerel 
(§ 2 94) and others is a simple ex- 
ample, the electrodes are charged up 
to a certain potential bj means of a 
battery, and then the latter is re- 
moved The instrument is so con- 
structed that when charged m this 
manner, one of the electrodes, acting 
as an indicator, moves with respect to 
its discharged position The entry of 
ionizing particles mto the chamber re- 
sults m the formation of lon-pairs 
which are attracted to the oppositely 
charged electrodes As a result the 
latter are discharged and the change 
m position of the indicator electrode is 
observed The rate of movement is a 
direct measure of the rate of entry 
of ionizing radiations, and the total 
change in position of the indicator is 
related to the total amount of radiation 
entering the chamber 
6 16 One of the simplest and gen- 
erally useful devices of the electrostatic 
type of ionization chamber is the 
quartz fiber electroscope invented by 
C C LauntsenandT Launtsen in the 
United States m 1937 It consists of a 
very fine metal-coated, quartz fiber, 
about 6 mm m length, parallel to a 
rigid horizontal metal wnre to which it 
IS connected This is moimted withm, 
but insulated from, a cylindncal alu- 
minum case which acts both as the 
ionization chamber and one of the 
electrodes The system of fiber and 


rigid ivire, which represents the other 
electrode, is charged with respect to 
the metal case by connecting for a 
short time to a battery of 100 to 200 
volts As a result of the repulsion 
between the rigid metal wire and the 
flexible fiber, the latter, which acts as 
the indicator, is displaced from its 
normal position When the electro- 
scope IS exposed to lomzmg radiations, 
the charged wire and attached fiber 
collect ions which reduce the charge, 
hence the mutual repulsion decreases 
and the fiber gradually returns to its 
ongmal position The rate of move- 
ment, observed by means of a micro- 
scope wnth a scale m the eyepiece, is 
roughly proportional to the rate at 
which the ions are collected, and hence 
to the rate of entry of the lomzing 
radiations 

6 17 The chief use of the Launtsen 
electroscope is as an integrating instru- 
ment to determine the total amount of 
lomzing radiations emitted by a gi\en 
material in a certain tune This is 
measured by the total movement of the 
flexible fiber indicator As a general 
rule, beta and gamma rays can pene- 
trate the thin aluminum wall of the 
ionization chamber, but for beta rays 
of low penetrating power, and par- 
ticularly for alpha particles, a thin 
'‘iTindow” may be used, or the speci- 
men under examination may be placed 
within the chamber 

6 18 In the second method of using 
the ionization chamber to determine 
the total ionization produced by either 
alpha, beta or gamma radiation, the 
battery is left connected to the elec- 
trodes, as m Fig 6 3 By suitable 
design of the instrument, the pro- 
duction of ion pairs results m a very 
weak, but continuous, flow of current 
which can be measured by means of 
a sensitive electrometer, e g , of the 



Measurement of Radioadiiniy 


135 


Lindemahn type, or by a vacuum- 
tube instrument. The current strength 
is directly proportional to the rate at 
which radiation is entering the ioniza- 
tion chamber. 

6.19. If it is required to determine 
beta radiation in the presence of alpha 
particles, the rays are permitted to 
enter the ionization chamber through 
a "window” made of a thin sheet of 
aluminum. This is sufficient to prevent, 
the passage of alpha particles without 
appreciably hindering the beta radi- 
ation. However, allowance must be 
made for gamma rays if they are 
present, 

6.20. Ionization chambers for ganama 
rays usually contain a heavy gas, such 
as argon or difluorodichloromethane 
("Freon”), often at liigh pressure, so as 
to facilitate the liberation, by each 
gamma-ray photon, of an electron 
capable of producing ionization. If 
alpha or beta particles arc present, as 
they frequently arc, they may be cut 
out by means of a thin sheet of lead 
which stops these particles but has 
little influence on the gamma rays. 

PnopoimoNAU Counters 

6.21. Although the ionization cham- 
ber method of measuring radioacti\dty 
is vety simple .and convenient, it has 
the disadvantage of requiring the use 
of a verj’ sensitive electrometer or of 
a powerful vacuum-tube amplifier. 
Other ionization instruments have 
therefore been demsed in which there 
is a considerable degree of internal 
amplification. It can be seen in Fig. 
6.2 that if the potential .applied to an. 
ionization ch.ambcr e.Kceeds a certain 
Value, the pulse size is no longer con- 
stant, but incre.ascs with the voltage. 


The condition is now that represented 
by region III, known as the proportional 
region. It is best attained by using a 
cylindrical chamber, which acts as the 
negative electrode (cathode), with a 
central wire as the positive electrode 
(anode). When the voltage is high 
enough the potential gradient near the 
central ivire becomes so large that the 
electrons, produced in the primary 
ionization of the gas by an alpha or 
beta particle, will move toward it with 
a very high speed. In region III this 
speed becomes great enough for the 
electrons to cause the ionization of 
other atoms and molecules in the gas; 
the electrons so produced may cause 
further ionization, and so on. This 
multiplication effect is often referred 
to as a Townsend avalanche or Tomh- 
send cascade, in honor of its discoverer, 
J. S. Towmsend (see § 6.1).* 

6.22. An electron from each original 
or primary ion-pair may consequently 
lead to the formation of a large number 
of secondary ion-pairs. The total num- 
ber of ion-pairs produced by a single, 
primarj’' ion-pair is called the gas- 
amplificalion factor. This factor is unity 
in the ionization chamber (region II), 
but it may become as large as 10® to 10® 
in region III. The size of the pulse 
produced by a single particle is thus 
increased enormously; it can then be 
registered by means of a sensitive elec- 
trometer or it may be used, in con- 
junction with a vacuum-tube amplifier, 
to operate a mechanical coimter. Pro- 
added the voltage is maintained at a 
steady value, the amplification, factor 
remains constant and the size of the 
pulse is proportional to the number of 
primarj’’ ion-pairs produced by the 
entering ionizing particle. This is why 


thought that the avalanche ionization was produced bv the positive 



13G Sourcehooh on 

region III is referred to as the pro- 
portional region, and counters oper^ j 
atmgm this region of voltage are called , 
proportional counters ' 

6 23 As already indicated, the in- | 
strument consists of a cylindrical tube | 
ivith a central wire, the latter being ■ 
attached to the positive pole of the | 
battery The magnitude of the applied | 
potential depends on the conditions, 
but it may be from 500 to 800 volts, or I 
more The gas for filling proportional i 
counter tubes is generally a mu'rture of ' 
methane and 10 to 25 per cent of aigon | 
The argon increases the amplification | 
factor but the methane makes the in- 
strument more stable in operation 
The pressure of the gas is usually less 
than atmospheric, although a success- 
ful proportional counter for charged 
particles has been descnbed in which 
methane gas at atmospheric pressure 
flows continuously, the experimental | 
matenal being inside the counter tube 
6 24 Because of the proportional 
character of the amplification, an alpha 
particle will give a larger pulse than 
will a beta particle or a gamma-ray 
photon, ]ust as in the ionization cham- 
ber Hence proportional-counting in- 
struments are particularly useful for 
counting alpha particles in the pres- 
ence of beta particles and gamma rays 
As stated in § 6 14, by means of suit- 
able devices, the smaller pulses can be 
Ignored and only the larger pulses pro- 
duced by alpha particles recorded 
The proportional counter can also be 
used for the measurement of beta par- | 
tides alone or in the presence of alpha 
particles, as descnbed in connection ! 
with ionization chambers The ad- | 
vantages of the proportional counter 
he in the considerable internal ampU- ■ 
fication and the high counting rates i 
obtainable, but its chief weakness rests 
m the fact that the amplification factor 
depends on the applied voltage, and 


Atomic Energy Chap Y1 

this must be maintained constant 
within fairly narrow limits 

Geiger-Mi}llt:r Counters 
6 26 The type of instrument most 
widely used m radioactive counting at 
the present time is known as the 
Geiger-Muller counter, a name often 
abbreviated to Geiger counter or to 
G-M counter Because the detecting 
portion IS commonly m the form of a 
tube, the names Geiger-Muller tube or 
G-M tube are frequently used These 
instruments operate in region V of the 
curve, m Fig 6 2, show mg the van- 
ation of pulse size with the applied 
potential The conditions in region 
IV, which lies between the propor- 
tional and Geiger-Muller ranges, have 
found no application m radioactive 
studies, and in region VI the potential 
IS so high that once ionization takes 
place m the gas there is a continu- 
ous discharge of electricity, so that it 
cannot be used for counting purposes 
6 26 The advantageous character- 
istics of the G-M region can best be 
understood by imagmmg a weak source 
of ionizing (alpha, beta or gamma) 
radiation placed near an mstrument, 
similar to a proportional counter, con- 
sisting of a cylindrical negative elec- 
trode (cathode) with a central wire as 
the positive electrode (anode) This 
instrument is connected wth a device 
capable of indicating only relatively 
large pulses, but not smidl ones As 
the potential applied between the elec- 
trodes IS increased the number of 
pulses recorded per minute will be 
observed to change in the manner de- 
picted in Fig 6 4 Until the voltage 
reaches the value indicated as the 
stcaiing potential, the pulses are too 
Small to be detected But with rising 
potential the gas amplification in- 
creases, and pulses are recorded in 
increasing numbers Eventually, w hen 



Measurement of Radioactivity 


f he Geiger threshold ■potential is reached, 
corresponding to the beginning of re- 
gion V in Fig. 6.2, the number of pulses 
per minute becomes essentially con- 
sliinb, as indicated by the horizontal 
portion of the cun’e in Fig. 6.4. The 
range of potential over which this 
occurs is called the Geiger plateau. 
Beyond the plateau, continuous dis- 
charge (region VI) takes place, and 
counting is not possible. 



F/n. G.4. Variation with apiilied voltage 
of number of pulses received per minute 
due to ionising radiation. 

6.27. nie voltages of the threshold 
potential and of the plateau range 
depend, as may be c.\pected, on the 
design of the counter and the nature 
and pressure of the gas it contains, 
hlost G-hl counters are filled with 
gas at pressures below atmo.spheric, 
and the plateau may then extend 
over a range of Vvo or three hun- 
dred volts in the region from about 
SOO to 1500 volts. The operating voU~ 
ape is tisually chosen so as to he some- 
what less than the value at the middle 
of tiie plateau. In the curve shown in 
I'ig. 6.4 the plateau is represented as 
loruontal; this is an ideal situation, 
but in actual praclire there is often a 
a ight Upward slope. Tlie slope must, 
however, be small if the G-U counter 
« to he satisfactorj', for one of its 
uuportant advantages is that the num- 


137 

ber of pulses registered per minute 
from a given source remains constant 
in spite of possible variations in the 
voltage; this condition can be realized 
only if the plateau is reasonably level, 
as in Fig. 6.4. 

6.28. The essential difference be- 
tween the proportional and the Geiger 
regions is that in the former an electron 
from an ion-pair probably produces an 
avalanche at one point only, whereas in 
the G-M region the avalanche spreads 
along the ivhole length of the central 
wire. The pulse size in the propor- 
tional region thus varies with the num- 
ber of primary ion-pairs, but in the 
Geiger counter the amplification is so 
great that the size of the pulse is 
almost independent of the number of 
ion-paim. Although the amphfication 
in the Geiger region is large, the dis- 
charge is not continuous, as it is in 
region VI, The negative members of 
the ion-pairs are mainly electrons, and 
these reach the central wire anode in a 
very short time. The positive ions, 
consisting of charged gas molecules, 
however, move much more slowly 
toward the walls of the tube, which act 
as the cathode. As a result a positive 
space charge is built up near the anode; 
the effective potential difference in its 
vicinity is consequently decreased and 
the discharge is terminated. 

6.29. Because the pulse size in a 
G-M counter is essentially independent 
of the number of primary ion-pairs, it 
is unable to distinguish between alpha 
and beta, or other ionizing, particles. 
However, the Geiger tube is rarely 
used to count alpha particles, and if 
these are present together with the 
beta particles, they can be readily cut 
out, as described in §6.19. An im- 
portant advantage of the G-M counter 
is that the gas-amplification factor 
may attain a value as high as so 
that pulses are obtained which require 




138 

little external amplification Although 
Geiger counters are simple and con- 
venient m many respects, thej some- 
times behave m an erratic manner 
6 30 In view of the great interest 
m G-M counters at the present time, 
it may be mentioned that the principle 
was first used by Rutherford and 
Geiger in 1908 to count alpha par- 
ticles with the object of determining 
their charge (§ 2 106) The apparatus 
consisted of a brass cyhnder, about 
20 cm long and 17 cm internal diam- 
eter, with a thm central insulated wire 
which was attached to the positive 
terminal of the battery “In our 
experiments," they said, “it was ar- 
ranged that the alpha particles could 
be fired through the gas at low pres- 
sure exposed to an electric field some- 
what below the spaiking value In this 
way, the small ionization produced by 
one alpha particle in passing along 
the gas could bo magnified several 
thousand times The sudden current 
through the gas due to the entrance of 
an alpha particle in the testing vessel 
was thus increased sufficiently to give 
an easily measurable movement of the 
needle of an ordinary electrometer " 
With this apparatus Rutherford and 
Geiger were able to count the alpha 
particles from a radium C source 
6 31 In 1913, some improvement m 
the construction of the tube was made 
by Geiger, but the modem highly 
sensitive form is essentially that de- 
signed by Geiger m collaboration with 
W Muller in Germany in 1928 It 
should not be overlooked, however, 
that the wnde sphere of usefulness of 
the G-M tube, as well as the ionization 
chamber and proportional counter, 
owes much to the developments in 
vacuum-tube circuits which have taken 
place in recent yeara 
632. One of the troublesome fea- 
• Other factors, which need not be 


Chap VI 

tures of the Geiger-Muller counter is 
that when an ionizing particle produces 
an avalanche the resulting discharge 
pulse IS liable to continue for some 
time If another particle enters the 
counter tube before the discharge is 
complete, the pulse it should produce 
will bo confused with the preceding 
one, and so on for subsequent pulses 
In other w ords, the separate pulses are 
not resolied, ond hence cannot be 
counted The continuation of the dis 
charge or, more correctly, the for- 
mation of a multiple discharge appears 
to be due to the posit ve ion members 
of the ion pairs When they reach the 
walls, i e , the cathode, of the G-M 
tube, the positive ions cause electrons 
lo be liberated, these move rapidly 
toward the central wire, and thus re- 
new the discharge previously termi- 
nated, as described above 

6 33 There are two main procedures 
for suppressing or guenchrng the dis- 
charge, BO as to improve the resolving 
power of G-M counters In the sel/- 
quenchtng, or internally quenched, type 
the filling gas is a mixture of argon and 
a few per cent of a polyatomic organic 
gas or vapor, such as methane, ethane 
or ethyl alcohol The purpose of the 
argon is to provide high specific ioni- 
zation and a low starting potential, 
while the organic molecules quench the 
discharge Because the quenching 
compKiund lomzes more readily than 
argon, the positive argon ions initially 
formed transfer their charges to the 
organic molecules, so that virtually 
only ions of the latter reach the walls 
of the Geiger tube As a result, the 
energy which would otherwise have 
caused the emission of electrons is now 
used to decompose the molecules of 
quencher * 

6 34 Some of the decomposition 
products deposit on the walls of the 


inentioDed here, are also operative 


Sourcebook on Atomic Energy 


Measurement of Jtadioaclivity 


139 


counter and on the central wire, and 
this sets a liniit to the life of self- 
quenching counters; nevertheless, a 
good tube may count as many as a 
billion, i.c., 10’, pulses before becoming 
ineffective. It can then be opened, 
cleaned and refilled, if desired. A new 
development is the use of a halogen 
gas, such ns chlorine or bromine, as 
a quencher in place of an organic com- 
pound. St*lf-qucnched tubes of this 
type have a relatively low threshold 
potential; they are said to have a 
virtually unlimited life, since the atoms 
produced by decomposition of the 
halogen molecules recombine to form 
the molecules once again. A patented 
G-M tube containing argon, ndth small 
amounts of xenon, oxygen and nitro- 
gen, is claimed to be self quenching 
and to have infinite life. 

6.36. The gas in the nonself-quench- 
ing type of Geiger counter is argon of 
98 per cent, purity, the small amount of 
impurity being possibly advantageous. 
The quenching of the discharge is now 
achieved by means of an external re- 
sistance or by the use of an auxiliary 
vacvium-tube circuit. These automati- 
cally reduce the voltage below the 
starling potential after each pulse, and 
then restore it in time for the next 
pulse. Since there is no decomposition 
of the gas, an externally quenched 
counter of this type has a very^ long life. 

6.36, IMicn proj^erly quenched, in- 
ternally or externally, a G-M counter 
vrill have a recovery, or resolving, time 
of about 2 X 10~^ second; that is to 
say, ))ariic!es arriving at intenmls of 
not loss than 2 X 10“* second niU give 
separate pulses. If the particles were 
ptxxluccfl at a uniform rate, that is, at 
reg\ilar intervals, a maximum of 5000 
pulses could be counted per second. 
Howover, the emission of radioactive 
particlc-s is random in character and by 
no mc.ans uniform; consequently, the 


practical counting rate is below this 
maximum. In any event, there is al- 
ways a probability that two or more 
particles will arrive at such short in- 
tervals that they are not counted 
separately, and a correction must be 
made for such losses. This “coinci- 
dence” correction increases mth the 
resolving time of the tube and with the 
actual counting rate. 

6.37. For very fast counting it is 
necessary to use a suitable scaler in 
conjunction wth the Geiger counter. 
Alternatively, a counting-rate meter 
may be employed (§ 6.13). 

central wire (ANODE) 


z 


WETAL CYLINDER (CATHODE) 

Fig. 6.5. Construction of simple Gciger- 
Miiller tube. 

6.38. Because of their versatility, 
G-M tubes have been made in a great 
variety of sizes and shapes, from 1 cm. 
to 1 meter in length and from 0.3 cm, 
to 10 cm. in diameter. The walls can 
be of metal such as copper, or a metal 
cylinder may be supported inside a 
glass tube (Fig. 6.5). Another possi- 
bility is to coat the interior surface of 
the glass tube noth a thin layer of an 
electrical conductor, such as silver or 
graphite. The central wire which acts 
as the positive electrode (anode) is 
usually of tungsten, nith a thickness of 
0.02 to 0.05 mm. As indicated above, 
the nature of the gas depends on the 
t3q>e of counter; the pressure is usually 
less than atmospheric, but in some 
cases it is the same as that of the 
atmosphere. Geiger-Miiller counters 
have been designed for the measure- 
ment of alpha and beta particles and 
neutrons, and also for gamma and 
X-raj’s. TTiey are, however, mainly 






140 


SouTcebooh on Atomic Energy 


used for beta and gamma rays, be- 
cause it IS difficult to make tubes with 
windows thin enough to be penetrable 
by alpha particles Wlien the source 
of the beta radiation is weak, or the 
penetrating power is small the ma 
ternlunderexammationmaj be placed 
inside the counter or the latter may be 
made with a very thin glass or mica 
window, which the particles can pen 
etrate 

639 In the majority of instances 
Geiger-Muller counters are used for 
comparison purposes so that it is not 
important to know the geometrical 
efficiency or geometry, i e the fraction 
(or percentage) of the total number of 


Cha-p VI 

particles emitted by the source that 
actually enters the counter tube All 
that IS required is that the geometry 
should be the same in all cases If 
absolute counting is being undertaken, 
then the geometiy of the instrument 
must be known, and this can be deter- 
mined, at least approximately, by the 
use of a standard radioactive source 
Alpha particle standards can be pre- 
pared from uramum, and*beta and 
gamma standards can be obtained It 
should be mentioned here that the 
foregoing considerations concerning 
relative and absolute counting apply 
equally to ionization chamber and pro- 
portional counters 


MEASUREMENT OF RADIATION BY OTHER METHODS 


SctNTILIATION COUNTERS 
6 40 In the course of his early 
studies of radioactivity H Becquerel 
found m 1899, that the radiations, 
like X-rays and cathode rays, are 
able to produce luminescence in a 
number of substances, such as zme 
sulfide (Sidot s hexagonal blende), bar- 
ium platmocyanide and diamond This 
property of radioactive rays which is 
mainly due to the alpha particles, was 
employed by Curie and by Debieme 
in the studj of the gaseous emanations 
(§ 5 18) In 1903, W Crookes m Eng- 
land, and J Ulster and H Geitel m 
Germany, independently reported that 
the luminescence produced by alpha 
particles on zinc sulfide was not uni- 
form but consisted of a large number of 
individual flashes which could be seen 
m a microscope * A year later, m the 
first edition of Ins book on Radioactivity, 
Rutherford wTotc “In the scintil- 


lations of zmo sulphide, we arc actu 
ally witnessing the effect produced by 
the impact of single atoms of 
matter [i e , the alpha particles] 

This would offer a very convenient 
means of actually counting the niunber 
of the particles if each particle 
gave rise to a flash of hg^it ’ At the 
time, Rutherford did not think this 
was very probable, but later, in col- 
laboration with Geiger, he proved that 
such was actually the case 
6 41 The first attempt to count 
alpha particles, by obsen mg the scin- 
tillations they generated in a diamond, 
was made by E Regener in Germany 
in 1908 At about the same tune, 
Rutherford and Geiger compared the 
number of scintillations produced by a 
radium 0 source on a zinc sulfide 
screen with the pulses m an electneal 
(Geiger type) counter The numbers 
Were approximately the same m both 


• Crookes devised a small instrument which 1 e called a spmthanscope (from the Greek 
aptnlharts a spark) for making these scintillations visible It consisted of a brass tube with 
a zinc sulfide screen at one end with a speck of radioactive salt I mm from it and a lens 
at the other end Similar scint illat ions can often be seen by observing the figures on a luminous 
w alch dial with a lens in the dark 


Mcasuremonl of lladioaclivity 


cofios, so that if each alpha particle 
caused a single pulse in the counter, 
then it also gave rise to one scintil- 
lation. In this manner Rutherford and 
Geiger established the reliability of the 
scintillation method of counting alpha 
particles. The procedure vas used by 
Geiger and Mar-sden in their original 
work in 1910 on the scattering of alpha 
particles during passage through thin 
sheets of metals (§ 4.9), and also later, 
in 1913, in their confirmation of Ruth- 
erford's equation, based on the nuclear 
theory of the atom (§4.13). It was 
also employed by Chadwick and others 
for the determination of the nuclear 
charge by the method described in 
§4.27. 

6.42. Prior to the 1930s, when the 
development of vacuum-tube circuits 
simplified electrical counting and de- 
tection, the scintillation method, in- 
volving tedious visual observation, 
was virtually the only procedure used 
for both quantitative and qualitative 
studies of alpha particles. As a result 
of the progress made in the methods of 
counting, described above, the scin- 
tillation procedure was largely dis- 
carded. However, in recent times there 
Ians been a revival of interest in the 
subject because of the advent of the 
electron-multiplier tube with a photo- 
electric cathode, sometimes- called a 
pholomvUiphcr tube. The light pro- 
duced in a single scintillation, which 
Js too feeble to measure directly, is 
allowed to faU on the cathode of the 
multiplier tube. A number of elec- 
trons arc released as the re.sult of the 
photoelectric cfTcct, and these are 
greatly increased in the successive 
t^‘age.s of the multiplier tube, so that 
uUitnately a measurable current pnlse 
vill be produced. This can be re- 
corflcfl, after further mnplification if 
necess.arj', in the manner described in 
)>remring .sections. 


141 

6.43. In addition to the scintillation 
counters for alpha particles, similar 
detectors are being developed for beta 
and gamma rays. Some of these use 
inorganic materials, such as calcium 
tungstate (Scheelite) and alkali halides 
containing traces of thallium, but of 
particular interest is the emplojonent 
of solid naphthalene (H. Kallmann, 
1947), .and certain other hydrocarbons. 
These organic compounds have the 
unusual property of being transparent 
to the luminescence (fluorescence) pro- 
duced in them. In the detector a clear 
layer of naphthalene or, better, anthra- 
cene, chrysene or stilbene, is placed 
between the source of beta or gamma 
rays and the cathode of the photo- 
multiplier tube. The radiations pass- 
ing into the crystal produce scintil- 
lations which then proceed to the 
multiplier tube and are recorded as 
pulses. A device of this type is sensi- 
tive to particles arri\nng at the rate of 
the order of a million per second, so 
that veiy rapid counting is possible. 
This method of scintillation counting 
with the aid of a photomultiplier tube 
has many advantages and it is finding 
increasing applications, especially for 
the measurement of gamma radiation. 

Crystal Conduction Counters 

6.44. A new method of radiation 
counting, which may prove of interest, 
w\as proposed by P. J. Van Heerden in 
Holland in 1945. It has been knorni 
for some years that certain crystals, 
which arc normally poor electrical con- 
ductors, become — like gases — conduct- 
ing when exposed to ionizing radi- 
ations. If the crystal is placed between 
two electrodes, to which a potential is 
applied by means of a b.attery, each 
ionizing p.arlicle will produce a pulse 
of current which can be amplified and 
recorded. Van Heerden employed a 
silver chloride cr 5 'stal, but this has 



142 Soutc^ooK on 

to be cooled m hqxiid an in order to 
be effective Later it ivas found that 
some, but not all, diamonds can re- 
spond to gamma, and probably to beta, 
radiations at ordinary temperatures 
It IS claimed that extremely short 
pulses are obtained, so that much more 
rapid recording is feasible than with 
theusualGeigei Mullercounter There 
IS no doubt that substances, other than 
silver chloride, which must be used at 
Ioi\ temperatures, and diamond, winch 
IS costly, will be found m due course 
that respond m a similar manner to 
beta and gamma rays If bo, the 


Atomic Energy Chap VI 

crystal counter may well have an im 
portant role m the future 

6 46 In view of the increasing im- 
portance of radiation measurement m 
vanous aspects of atomic science and 
the occasional unsatisfactory behaiior 
of Geiger tubes, which are now so 
widely used, the development of new 
principles for the counting of particles 
and photons is of considerable interest 
It will probably be found that no single 
device is best for measurements of all 
types, but each instrument will prove 
to have its own sphere of usefulness 


TRACKS OF IONIZING PARTICLES 


Ions as Condensation Nuclei 

6 46 While ionization chambers, 
Geiger tubes, and other devices have 
proved invaluable for counting ioniz- 
ing particles another instrument — the 
Wilson cloud chamber — has played a 
part m the study of such particles 
which, although somewhat different, is 
nevertheless equally significant The 
fundamental principles involved m the 
cloud chamber were discovered by the 
English physicist C T R Wilson in 
1896 Like J S Townsend, whose in- 
vestigations led to the development of 
methods for counting alpha and beta 
fiartjcJfs Wjison 

in the famous Cavendish Laboratory, 
presided over at that time by J J 
Thomson However, it was not until 
1911 that Wilson devised the first form 
of the instrument w hich made possible 
the discmery of the positive electron, 
or positron, as described in § 2 67, and 
also of the still mysterious meson, to 
which reference will be made in Chap- 
ter XVII 

647. Air contained m an enclosed 
space can be saturated with the vapor 
of water or of any other liquid, the 


amount of the vapor necessary to pro- 
duce saturation decreasing as the tem- 
perature 15 lowered Imagine a vessel 
A containing air saturated with water 
vapor enclosed by a piston B, which is 
maintained m position by the pressure 
of the air below it (Fig 6 6) Suppose, 
that by means of a valve C, the pres- 
sure under the piston B is suddenly re- 


5 ^ 



C 

Fia 6 6 Diagram of Wilson cloud 
chamber 


leased so that it falls, this w ill result m 
an instantaneous expansion of the gas 
m A The sudden (adiabatic) expan- 
sion will result in the air being cooled, 
so that it now contains more water 
vapor than is necessary for saturation 
at this lower temperature If particles 
of dust are present in the air, they wll 
act as condensation nuclei, and the ex- 



143 


Meafinrcmimt oj JiadioacUmiy 


cess of water vapor will separate out as 
fine dro])lcts of liquid in the form of a 
cloud or mist. If, on the other liand, 
there are no dust particles, the air will 
become supersaturated with vapor, 
and no condensation will occur unless 
there has been considerable expansion 
accompanied by a marked fall of tem- 
perature. 

6.48. In 1887, the versatile German 
physicist H. von Helmholtz, and oth- 
ers, had found that electrification 
brought about condensation in steam 
jets, and J. J. Thomson in 1893 had 
provided a theoretical interpretation of 
thc.se facts. But it was C. T. R. Wilson 
who, in 1896, discovered that when 
rlusbfree air saturated with water va- 
por wsis exposed to X-rays, it behaved 
on expansion just as if it contained 
dust particles. Later he showed that 
the radioactive radiations from ura- 
nium and the electrons produced by 
the photoelectric effect of ultraxdolet 
light on zinc (§ 2.48) had a similar in- 
fluence. Wilson suggested that the 
positively and negatively charged ions 
fonned in the air bj'' the radiations 
acted, like dust particles, as condensa- 
tion nuclei, and this was confirmed 
when he proved that no condensation 
would take place on expanding the 
saturated air after the ions had been 
removed by an electric field. 

6.49. Tlic background of Wilson’s 
di.scovcry provides a striking example 
of the consequences of scientific emd- 
odty and obscrv.ation. In the addrc.ss 
uhieh he gave following the award to 
him^of the Nobel Prize for Phj'sics in 
1927, Wilson described hoAv in 1894, 
'"hen he was still a young student, he 

a few wcok-s during the summer 
*n the obsen-ators’ on tlie summit of 

k-n Nevis, in Scotland. ^‘Tlic wonder- 
ed optical phenomena shown when the 
shone on the clouds . . . he 
satd, “greatly c-\cUcd my interest, and 


made me wish to imitate them in the 
laboratory’. At the beginning of 1895, 
I made some experiments for this pur- 
pose — making clouds by expansion of 
moist air. . . . Almost immediately I 
came across something which promised 
to be of more interest than the optical 
phenomena which I had intended to 
study’.’’ At the beginning of 1896, Wil- 
son had access to an X-ray tube, a 
novelty which was attracting great in- 
terest among scientists at the time, 
and it was then that he discovered the 
effect of ionizing radiations in facili- 
tating the condensation of water drop- 
lets in saturated air cooled by expan- 
sion. Thus, he turned away from the 
study of the colors produced when 
light is scattered by clouds, to investi- 
gate the phenomenon of condensation 
on gaseous ions which has proved of 
such great value in many aspects of 
nuclear science. 

The Wilson Cloud Chamber 

6.60. C. T. R. Wilson’s discovery 
was first put to practical use in the 
early’ attempts to determine the mag- 
nitude of the electric charge carried by 
gaseous ions. Observations were made 
on the clouds produced w’hen air satu- 
rated with water vappr was exposed to 
various ionizing radiations, and then 
cooled by sudden expansion, as indi- 
cated in § 2.31. It was in 1911, how- 
ever, that Wilson showed that the path 
of a single ionizing particle could be 
rendered visible. The apparatus, which 
has become known as a cloud chamber, 
for the obvious reason, is similar in 
principle to the device depicted in Fig. 
6.6. The air is saturated with water 
vapor and the piston is allowed to drop 
to such an extent as will expand the 
volume of the air by a factor of 1.25 to 
1.37, this being the range in which 
cloud formation can occur. 

6.61. If an ionizing particle enters 



144 


Smtrcelxiok on Atomic Energy 


the chamber either immediately before, 
during or immediately after the expan- 
sion, the trail of ions left in its path 
will act as condensation nuclei, so that 
a close array of fine droplets, i.e., a 
kind of linear cloud, called a clxntd 
track, will be formed. By using suitable 
strong illumination D from the side, 
the track appears as a white line on a 
dark background. This can be photo- 
graphed by means of two cameras at 
right angles, as shown at E and F, so 


Chap. VI 

cations in the study of ionizing parti- 
cles, radiations and even neutrons, to 
which reference will be made in the 
course of this book, the Wilson cloud- 
chamber photographs have a signifi- 
cance that is fundamental to the 
atomic theory as a whole. As Lord 
Rayleigh (4th Baron) has pointed out, 
while it is true that the Broivnian 
movement (§ 1.58) gives a magnified 
picture of molecular motion, that the 
Geiger counter permits individual 



FiQ. 6.7. Cloud tracks produced by alpha par- 
ticles from polonium. 


that 0 permanent record can be ob- 
tained from which the path of the wn- 
gle ionizing particle in three dimen- 
sions can be studied. 

6.52. The cloud tracks produced by 
a group of alpha particles are shonm in 
Fig. 6.7. It is seen that, in general, the 
particles travel in straight lines, al- 
though near the end of their paths, 
when their speeds have been greatly 
diminished, the particles are liable to 
suffer deflection, presumably as the re- 
sult of impacts with the nuclei of oxy- 
gen or nitrogen present in the sh. 

6.63. Apart from their many appli- 


alpha particles and electrons to be 
counted, and that flashes produced by 
single dpha particles are rendered 
visible in the Crookes spinthariscope 
(§ 6.40 footnote), it is the cloud track 
which provides perhaps the most con- 
vincing evidence of the reality of the 
atom. The track produced by an alpha 
particle indicates the path of a single 
helium nucleus, and deviations from & 
straight line show exactly where an en- 
counter with another atomic nucleus 
has occurred. 

6.64. Since the construction of the 
firat Wilson cloud chamber in 1911, the 




McQfiuroJ^CTit of Bodioachinty - 1 


apparatus has been improved in many 
u-ays, although the fundamental prin- 
ciple remains unchanged. In order to 
record rare nuclear phenomena, it is 
ncccssarj' to take many photographs, 
and in 1921 the Japanese physicist, T. 
Shimiy.u, working in England, devised 
a means for doing this automatically. 
The piston of the cloud chamber was 
attached to an electric motor so that 
the appropriate expansion, followed by 
compression to the initial volume, took 
place at regular intervals of a few sec- 
onds. After each expansion a photo- 
graph of such tracks as may haA^e been 
formed was taken on a moving film, 
and then the chamber was cleared of 
charged particles by an electric field, 
so that it W1U3 ready for the next cycle 
of compre.ssion and expansion. Be- 
cau.se the expansion was not sufficiently 
sudden, the cloud-track photographs 
were somewhat blurred, but this diffi- 
culty was overcome by ?. hi. S. Black- 
ett, in England in 1927, by using a 
.spring mechanism in place of the motor 
to move the piston of the cloud cham- 
ber at regular intervals. 

6.56. Instead of operating the cham- 
ber continuously, so as to make sure 
that a recortl is olitained of any impor- 
tant event that may take place, cloud 
chambers, particularly those' used in 
thc^ study of cosmic rays (Chapter 
XVll), are frequentlj'- constructed so 
as to function automatically at the 
critical moment. Geiger counters are 
pkecrl at the top and bottom of the 
chamber and Avlien an ionizing particle 
piS'Cs through both of them, and 
neaee through the chamber, a relav is 
operated vhich causes expansion of the 
and condcn.salion of 'droplets of 
'V.iter on the ions left by the particle. 
The track of the latter is consequently 
O’ve.^ksl !)>• a photograph taken at the 
s-triic time. 

6.66, In the earlier cloud chambers a 


layer of water or oil was used on (he 
floor of the chamber as a seal for the 
piston, and this meant thao the instni- 
ment could be used only in the hori- 
zontal po.siiion. A decided advance in 
design was made by C. T. R. Wilson in 
1933 when he constructed a cloud 
chamber in which the piston was re- 
placed by a thin rubber diaphragm 
fixed at its edge. The diaphragm was 
maintained in a state of tension by 
means of compressed air in the back 
(or lower part) of the chamber, and 
wlien this was released the gas in the 
chamber underwent sudden expansion. 
A cloud chamber of this type can be 
used in any desired position. 

6.67. Although the foregoing de- 
scription has referred to water as the 
liquid used to saturate the air in the 
Wilson cloud chamber, it is more com- 
mon at the present time to employ 
eth}*! or propyl alcohol or a mixture of 
alcohol and water. The use of alcohol 
in this connection gives better conden- 
sation on positive ions than does water 
alone and, in addition, the extent of 
expansion necessary for droplet forma/- 
tion is diminished from 1.25 to about 
1.10 at ordinary pressures. T^Tiile air 
is the usual gas, cloud chambers con- 
taining argon are sometimes employed, 
and the pressure may range from be- 
low to well above that of the atmos- 
phere. 

6.68. A cloud chamber with gas at 
300 atmospheres pressure, i.e., about 
4500 pounds per square inch, has been 
designed for tbe study of certain 
cosmic-ray particles at the Brookhaven 
National Laboratorjf on Long Island, 
N. Y. It is hoped that by using gas 
under high pressure a larger number of 
these e.xtreraely energetic and pene- 
trating particles will come to the end of 
their path in the cloud chamber, and 
thus reveal their fate, YTien the ch.am- 
ber contains air at atmospheric pres- 



146 Sourc^ook on 

sure the \ast majority of the partides 
pass right through because of their 
great penetrating poM er 

6 69 For the studj of radioactz've 
radiations and for many similar pur 
poses relativeb simple cloud cham 
bers with air at ordinary pressure are 
quite adequate Because of the low 
penetrating power of alpha particles 
the source of the radiation must be m 
side the chamber but a substance 


Atomic Energy Chap M 

be determined and the nature of the 
particle identified an experienced ob 
server can thus dist nguish between an 
alpha particle a proton a meson and 
an electron The alpha particle has the 
highest specific ionization and gives a 
short dense track while an electron 
unless it IS moving with very high 
speed leaves a track that is diffuse and 
tortuous (Fig 6 8) By observing the 
curvature of the cloud track m a mag 



Fig 6 8 Fa nt cloud tracks produced by beta 
particles from radium E (The curvature of the 
tracks was caused by a magnetic field ) 


emitting beta particles can be placed 
outside and the rays allowed to enter 
through a window Gamma rays 
and X rays yield cloud tracks because 
they hberate electrons which produce 
ionization m their paths (§ 6 5) 

6 60 By making visible the actual 
track of an ionizing particle the cloud 
chamber permits the measurement of 
the range of the particle from which its 
energy can frequently be calculated 
(§ 7 20) Bj counting the drops m the 
cloud track the specific ionization can 


netic field the sign of the ionizing parti 
cle can be determined As seen in 
§ 2 69 this fact played an important 
role m the discovery of the positron 
Finally it may be mentioned cloud 
tracks have proved useful in the in 
vestigation of nuclear collisions and 
disintegrations (Chapter IX) 

Photogsaphic Detection 
OF Ionizing Particles 
6 61 In recent years there has been 
a marked revival of interest in the use 



Meamrement of Radioactivity 


147 


of pliotographic films and plates for the 
study of ionizing particles. It will be 
recalled that the phenomenon of radio- 
activity was discovered by Becquerel 
because of the action of the radiations 
on sensitized plates (§ 2.93), and many 
applications of this effect have been 
nwdc from time to time. It will be in- 
dicated in § 16.G1 how photographic 
methods are used to obtain "radioauto- 
graphs” which provide information on 
the distribution of radioactive ele- 
ments in plant and animal tissue, and 
in § 18.31, the emplojunent of film to 
determine the extent of exposure of a 
human being to radiation will be de- 
scribed. In the present section the 
matter to be considered is the direct 
recording on a photographic plate of 
the actual tracks of ionizing radiations. 

G.G2. As long ago as 1910, S. liino- 
shita of Japan, and in the following 
year, AI. Reinganura of Germany, 
showed that the silver halide grains of 
photographic emulsions are affected by 
alpha particles so that on development 
they are reduced to black specks of 
silver. The path of the alpha particle 
thus appears as a line of developed 
grains. Because of the relatively high 
density (stopping power) of the emul- 
sion, the tracks are extremely short as 
eojupared with those obtained in the 
Wilson cloud chamber. Although the 
pliotographic method was employed 
f<ir various purposes during the 1920s 
mid 1930s, it is only in recent years 
that the procedure has come into gen- 
cr.\l u.^c, largely as a result of the devcl- 
opjnont of special “nuclear plates.” 

6.63. The carh' investigators used 
ordinary’ photographic platca in their 
work, hilt in recent years the composi- 
tion of the emulsion h.as been changed 
as to make it more stiitable for the 
i-tudy of \Tirious ionizing particles, 
such as alpha particles, protons, mes- 
on^ and even electrons. By adding 


boron to the emulsion, neutrons can 
also be detected (§ 11.26). The emul- 
sions now used contain silver bromide 
to the extent of 80 per cent, or more, of 
the dry weight, this being about ten 
times the quantity present in plates or 
films used for normal photographic 
purposes. The silver halide grains are 
extremely small, about 2 X 10~® cm. 
in diameter. 

6.64. As stated above, the tracks 
produced in a photographic plate are 
very short, but they can be readilj’’ 



Fig. 6.9, Magnified tracks in a photo- 
graphic plate, produced by alpha particles 
from radiothorium and its successive decay 
products. (From ‘‘Nucleonics,” a McGraw- 
Hill publication.) 

magnified and photographed (Fig. 
6.9). With the new' emulsions the sil- 
ver grains are so distinct that they can 
be coxmted, and from the spacing, the 
nature of the ionizing particle respon- 
sible for a given track can be identified. 
Further, from the length of the track, 
which may not be more than a few 
thousandths of an inch, the energy of 
the particle can be estimated. 

6.65, Tlie photographic plate re- 
sembles the Wikon cloud chamber in 
the respect that it can record individual 
events invoking atomic nuclei and 
otliev charged particles. Tlie distinc- 
tion betw'een the appearance of the 
tracks })roduced by different particles 
is not so marked as in the cloud cham- 
ber, but^ with improvements in the 
composition of the emulsion, this dis- 



148 Sourcebook on 

crepancy ■vmU become less important m 
the course of time One of the merits 
of the cloud chamber is that it can be 
operated m a magnetic field and then 
the curvature of the track gives the 
sign of the ionizing particle This can- 
not be done with the tracks m a photo- 
graphic emulsion because it would re- 
quire extremely intense fields to make 
the curvature apparent The sugges- 
tion has been made, however, that two 
emulsion surfaces be placed parallel to, 
but separated by air gaps from, the 
one on which the track i\ ould normally 
appear If these plates are set in a 
magnetic field, the direction of curva- 
ture of the path of the particle in the 
air gap is indicated by which one of 
the outer emulsions now contains the 
track 

6 66 The advantage of the photo- 
graphic plate lies m its great simplicity 


Atomic Energy Chxip VI 

and m the fact that it is continuously 
sensitive, in other words, it is always 
ready to record an event, whereas the 
cloud chamber must be expanded at 
the appropriate moment Further, the 
photographic plate technique is equiva- 
lent to a high-pressure cloud chamber 
for the study of very penetrating par 
tides Because of the stoppmg power 
(§ 7 9) of the emulsion, which is about 
two thousand times that of normal air, 
the range of such particles is very much 
smaller than in a gas, even under pres- 
sure By using a stack of photographic 
plates the fate of these particles at the 
end of their paths can frequently be 
observed There is little doubt that 
many appbcations ivill be found for 
sensitive emulsions in atonuo nuclear 
studies of various kinds, some of these 
ivill be mentioned later m this book 
(Chapter XVII) 



Nuclear Radlaflons 


Chaffer VII 


THE PROPERTIES OF 

Range of Alpha Particles 

7.1. In the preceding chapter the 
various methods for studying alpha, 
beta and gamma rays Avere described 
JS appropriate, now, to return to a 
consideration of the properties of these 
nudcar radiations. It can be seen from 

chamber pho- 
tosraph of the alph,a particles emitted 

to ZT'" polonium, 

tnat the tracks are nearly all of the 

"'hjch they are 

nir^fh^ P'’o^iJcing ionization of the 
a.r through which they pass. 

Wo; thJIxSSre yeTergfby tlm 

is S -i ^ Circiunstances there 

ro^raS: 

hence the rn ionizing poAver, and 
Jots in the ^roP- 

•okZptaiZ S “ ‘“sin- 

P irticie ma'v n ^^Ph^ 

'hvtanceitUnfi^'^ defined as the 

io C and a pressure of 1 


alpha radiations 

atrn from its source to the point at 
which It can no longer produce appre- 
ciable ionization. 

7.3. Even before the invention of the 
cloud chamber pro\dded a means for 

fr«!S'''”Afr alpha-particle 

tracks, W. H. Bragg in England had 



° ' 2 3 < 5 ^r~r 

^ DISTANCE FROM SOURCE (CMl fi 

cun'e showing number 
of lon-pairs detected at various^disSes 
from a source of alpha partiefe 

these particles 
n i range. In 1904 he re- 

ported the results of an investigation 

befoftm "" ---tionThr: 

ler, of the specific ionization, i e the 

KHath ? W of 

vary AAdfb iT the cun-e 

i cITrvfif 

^1^ quite characteristic. As the 




150 


SoiircAooh on Atomic Energy Chap YU 


distance of the alpha particle from its 
source increases the specific ionization 
increases, at first slowly and then nioi« 
rapidly, reaches a maximum and then 
drops sharply almost to zero The dis- 
tance corresponding to the point R in 
Fig 7 1 represents the (extrapolated) 
range of the alpha particles from the 
gi\ en radioelement 

74 Jt isnofcdi/ficultto account, in a 
general 11 ay for the shape of the Bragg 
curve While the alpha particle trav- 
erses its path, producing lon-pairs as 
It proceeds, its energy, and conse- 
quently Its speed, steadily diminishes 
Because it moves more slowly, it 
spends more time m the vicinity of 
each of the molecules of the air which 
it encounters in its path and so the 
probability of removing an electron, 
and producing an lon-pair, increases 
The specific ionization thus increases 
steadily, at first, as the alpha particle 
moves away from its source Ulti- 
mately a point IS reached when elec- 
trons attach themseUes to the particle 
and convert it into a neutral atom 
which cannot cause ionization of the 
air, and so the specific ionization falls 
abruptly 

7.5 The reason u hy the end portion 
of the curve lo not vertical, but slopes 
slightly to the right, and may even 
have a slight “tail,” is that the alpha 
particles do not all lose exactly the 
same amount of energy in their encoun- 
ters with the molecules in their path 
Hence, they do not all cease to produce 
ionization at precisely the same dis- 
tance from their source This slight 
variation in the range, frequently re- 
ferred to as straggling, is also partly due 
to the formation of He+ ions, by the 
attachment of one electron to some of 


the alpha particles These ions stili 
possess ionizing pouer, and hence they 
cause a slight extension of the range 
before they take up a second electron 
and become neutral atoms 
7,6 Another vay of studying the 
rai^e of alpha particles is to determine 
the number which can be counted at 
vanous distances from the source For 
this purpose the latter may be placed 
on one plate (electrode) of an loniza* 



D STANCE fROM SbURCe ICMI A 


Flo 7 2 Rato at which alpha particles 
can be detected at vanous distances from 
a source 

tion chamber (§ 6 10) and counts taken 
with the other plate at vanous dis- 
tances away Alternatively, a scintil- 
lation counter, such as a zme sulfide 
screen, can be employed (§ 6 40) li 
the counting rate, say in pulses or scin- 
tillations per second, is plotted against 
the distance from the radioactive 
source, the result ^vlll be of the form 
shown by the curve m Fig 7 2 Up tc 
a certain distance the counting rate re- 
mains essentially constant, and then it 
drops sharply to zero, apart from slight 
straggling The extrapolated range » 
again indicated by the point R, 
greater distances the alpha particlei 
can no longer be detected * Where 


* The extrapolated wgc in Pjg 7 2 is slightly different from that in Fig 7 1, but the di& 
crepancy is no more than a fraction of & nun and can be ignored for present purposes A 
meanranpe, corresponding approximately to the Huddle of the rapidly Ascending portion oi 
Fig 7 2, la sometimes recorded, jt is about 1 3 per cent less than the extrapolated range in th( 
same figure 




Nti clear Radiaiions 


cloud chamber studies have been made, 
the ranges observed are in close agree- 
ment with those obtained from direct 
ionization or counting measurements. 

7.7. The extrapolated ranges, in air 
at. 15°C and 1 atm. pressure, of the 
alpha particles from a number of radio- 
elements are recorded in the accom- 
jjanying table. For a reason which will 
.soon be apparent, the half lives are also 
included. The ranges are seen to vary 
from 2.8 cm. for thorium, the longest 
lived, to 8.6 cm. for thorium C', which 
has the shorte.st life of the natural 


Helative stopping power 


radioelements. The significance of this 
inverse relationship between the half 
live.s of alpha particle emitters and the 
ranges of the particles will be consid- 
ered below. 


151 

length; in a cloud chamber, on the 
other hand, the alpha particle tracks 
are usuallj'' from 1 to 3 inches long. 
The range of an alpha particle thus 
depends on the medium through which 
it travels. 

7,9. A quantity called the slopping 
power of the medium has been defined 
as the rate of loss of energy^ by an alpha 
particle per unit distance as it travels 
through the medium. For practical 
purposes, however, it is more conven- 
ient to employ the relative stopping 
power; thus for any material, 

(7.1) 

the same source of alpha particles being 
used in both instances. Actually the 
relative stopping power depends to 
some extent on the source of the parti- 
cles, but an approximate average value 


Range of alpha particle in air. 
Range of alpha particle in material 


Rant.es and Hai.e Lums of Ai.raA Particle Emitter-s 


ParliorJcjnr/ii 

Thorium (Th*”) 

Radium {Rji“q 

Radiothoriuni (Th’”) 

Radium A (Po*'*) 

Thorium A (Po"'*) . . . 
Radium C' (Po'"*) . . . 
Thorium C' (Po"’) . . 


Panffc Half Life 

2.8 cm. 1.39 X lO'" yr. 

3.3 1020 yr. 

3.9 1.9 yr. 

4.0 3.0 min. 

5.0 O.IG sec. 

0,9 1.5 X 10~* sec. 

S.6 3.0 X 10- sec. 


Stopping Power 

7.8. II was mentioned in Chapter II 
(§§ 2.96, 2,105) th.at alpha particles are 
unable to penetrate a few sheets of pa- 
per or a thin aluminum foil, yet they 
can travel through several centimeters 
of air. It is evident, therefore, that dif- 
fermit materials permit the passage of 
alpha particles to different extents, 
liie same general conclusion can be 
dnuYu from the statement in § G.G2 
that tlic tracks produced by alpha par- 
tic‘if-.s in a phologratihic emulsion are 
'’U.y a few thousandtlis of an inch in 


is generally employed. By finding the 
thiclcnesses of thin metal foils and of 
other substances, such as mica, which 
will just prevent the j^assage of alpha 
particles of known nmge in air, the 
relative stopping powers of these mate- 
rials can be determined. Some of the 
values obtained in this way are as fol- 
lows: 

Mira .Aluminum Copper Gold 

2000 1600 .1000 4800 

7.10. For many purposes, it is con- 
venient to exprc-as the .stopping power 



152 


Sourcebook on Atomic Energy Chap VII 


of a medium m an alternative form If 
the range m cm m a given medium is 
multiplied by the density m grams per 
cc , the result is the mass per unit area, 
1 e , grams per sq cm , which is equiv- 
alent to the thickness of material re- 
quired to ^top (or absorb) the alpha 
particles Smee tlie mass per unit area 
equivalent of the absorber thickness 
expressed in grams per sq cm is very 
small for solid absorbers, the result is 
multiplied by 1000, so that it is given 
in milligrams per sq cm , usually writ- 
ten as mg /cm * It is thus the common 
practice to define the eguivuUnt thick- 
ness* of an absorber in mg /cm *, thus, 

Equivalent thickness in. rag /cm * s* 
Range X Density X 1000 

7 11 The thickness which is equiv- 
alent in stopping power to 1 cm of air 
IS obtained upon dividing the quantity 
defined above by the range of the given 
alpha particles in air Upon comparing 
the result with equation (7 1), it is 
found that 


Thickness m mg /cm* equivalent to 
DeDBity^ W00_ 
Relative stopping power 


The values of this thickness for the 
substances whose stopping penverv 
were given above are then as follows 


Mica Aluminum Copper Gold 
1 1 1 62 2 26 3 96 xng /cm * 


This means that with aluminum, for 
example, a piece I sq cm in area of a 
sheet which has the same effect as 1 cm 
of air m slowing down alpha particles 
weighs 1 62 milligrams, whereas 1 sq 
cm of an equivalent ^eet of gold will 
weigh 3 96 milligrams 


7 12 From the conclus:on<? concern- 
ing the stopping powers of vanous ele- 
ment reached by W H Bragg m 1905, 
it can be shown that the equivalent 
thickness as defined above should be 
proportional to the square root of the 
atomic w eight of the element Thus, it 
is possible to state, as a fair approxima- 
tion, that the thickness in mg /cm * 
eqmvafent to I era of air m the absorp- 
tion of alpha particles is equal to 
0 304**^, where A is the atomic weight 
m the case of an elemental substance, 
or the average of the atomic weights of 
the constituent elements for a com- 
pound material This result is useful 
for calculating the extent of absorption 
of alpha particles in various media for 
which experimental data are not avail- 
able 

7.13 In the study of alpha particles, 
and other radiations, it is customary to 
use thm sheets of metal foil, particu- 
larly of aluminum, of knoivn thickness, 
as the absorber in place of air, the 
range m air can then be readily deter- 
mined if the equivalent thiclmess is 
known Suppose it is found necessary 
to place a sheet of aluminum of 1 60 X 
10~® cm thickness over a specimen of 
uranium I m order just to absorb the 
alpha particles The range of the par- 
ticles in alummum is thus 1 60 X 10^ 
cm , and if this multiplied by the den- 
sity of alummum, 2 70 grams per cc , 
and a factor of 1000, the result, often 
referred to as the “range m mg /cm *, “ 
IS 4 32 mg /cm * Conversely, if the 
range m mg /cm * in aluminum, for 
example, is known, the actual thickness 
required to stop the particles is found 
upon dividing by 1000 times the den- 
sity of alummum To obtam the range 
of the alpha particles in air, the range 
in mg /cm * is divided by the thickness 
of the alummum, m the same units, 


S by deSSr “ "ttackness ’ aUhouBb it i> really thiek 



Nuclear Radiations 


153 


equivalent tx) 1 cm. of air, i.e., 1.62 
mg./cm.'; thus, in the present case, the 
range in air is 4.30/1,62 = 2.66 cm,* 

Vklocity, Energy and Range 
OF Alpha Particles 

7.14. Tlio direct measurement of the 
energies of alpha particles is made by 
detennining the radius of their circular 
path in a magnetic field. As stated in 
§ 2.43, the equation (2.8), which relates 
tlic charge e, carried by a particle of 
mas.s m, to the velocity v and the ra- 
di\ts of curvature r of the path in a 
magnetic field of strength H (see Fig. 
2.2), is applicable to any charged parti- 
cle. For the present purpose it can be 
rearranged to take the form 

V =— Hr, (7.2) 

and since the charge on an alpha parti- 
cle Is known to be twice the unit elec- 
tronic- charge, and the mass is that of a 
helium nucleus, i.e., a helium atom 
minu.s two electrons, the evaluation of 
the velocity requires only the determi- 
nation of the radius r of the path of the 
particle in a magnetic field of strength 

7.16. The experimental arrangement 
Used for this purjiose, known as a 180° 
viagiuiic spectrograph, is shown dia- 
grammalicolly in Fig. 7.3. The radio- 
liciive source is pl.nced at R and the 
alph.a particles emerge in a narrow 
beam through (he slit S. As already 
.‘•ccn, air slows domr the alpha particles 
and so the apj)ar.attis is evacuated by 
pumping out the air. A magnetic field 
Oj known .strength, which acts in a di- 
metion perpendicular to the plane of 
the diagram, is then applied, and the 


alpha rays are bent through an angle of 
180° so that they fall on a photographic 
plate at P. From the position of the 
trace produced where the particles 
strike the plate the radius of curvature 
of the path can be determined, and 
hence the velocity of the particles can 
be calculated from equation (7.2), 

7.16, In recent years the magnetic 
spectrograph has been improved by re- 
placing the photographic plate by a 
Geiger-Muller or similar counter, the 
position of which is fixed, say at the 



Fig. 7.3. Diagrammatic representation of 
a magnetic spectrograph. 

point P. The magnetic field is then 
varied until the counter show's that the 
particles emerging from S are reaching 
P, and are then traversing a path of 
known radius. In the older, photo- 
graphic method the magnetic field was 
constant, and the path radius was dif- 
ferent for alpha particles of different 
energies; . in the newer modification, 
which is simpler and more accurate, 
the radius of the path is constant but 
the field 7/ is varied so as to make par- 
ticles of different energies follow the 
given path, 

7.17. The energy of an alpha particle 
is cssentiall}' kinetic in nature, that is 
to say, it is due almost entirel}' to the 
motion of the particle; hence the en- 
ergj' of an alpha particle may be taken 
as equal to (§ 3.5), w'here, as 


aluminum is_ known, viz., 1600, the same result oai 
:.Dm«unn, by the reUxL A" ii 

adoiurxl dojK-nds on the datk avad^Wc ^ 


» 2.66 cm. The portici 




3 54 Sourcdtoot on Atomic Energy Chap VII 

above, m is its mass and v its speed * It measurements of the relative speeds of 
IS for this reason that measurements of alpha particles from radium C after 
the velocity of alpha particles, as de- theyhadpassedthrough\anousthick- 
scribed above, are often referred to as nesses of mica of knonn stopping 
energy determinations The mass of an power relative to air From the results 
alpha particle on the atomic \%eight he concluded that the velocity v of the 
scale IS 4 0028, and hence the mass of a alpha particle at any point at a dis- 
single particle m grams is obtained tance x from the source could be ex- 
upon dividing by the Avogadro num- preyed by the equation 
ber, 6 02 X 10^ (§ 1 57) , the result is 

6 65 X 10“^* grim If the velocity w is r* = a{R ~ x), (7 3) 

expre^'sed in cm per sec , the kinetic 

energy of an alpha particle is X where R is the usual range of the parti- 
6 65 X ergs making use of the cles, os described m § 7 2 and a is a 

conversion factor given in § 3 81, this constant If x, the distance from the 
becomes 2 08 X 10~‘V Mev, with v source, is set equal to zero, the corre- 
still in cm per sec The initial veloci- spending xelocity, represented by lo 
ties of alpha particles from radioactive will be the initial \elocity of the alpha 
sources vary from about 1 4 X 10® to particles at the source, and then equa* 
2 2 X 10® cm per sec and hence the tion (7 3) ^comes 
corresponding energies lie m the range 

between 4 and 10 Mev tg » aR (7 4) 

7 18. Tlio size of the pulse produced 

by an alpha particle in an ionization-* This relationship, known as the Oetger 
chamber counter coupled wth a linear formula, although denied from meas- 
amplifier is a direct measure of tho urements on a single substance, radium 
number of lon-pairs formed, and henco later found to be generally ap- 

of the energy of the particle This has phcable to alpha particles from various 
been utilized in conjunction ivith the sources, the constant a having the same 
pulse analyzer, desenbed in § 6 14, to value, namely, 1 03 X 10”, m all cases, 
determine the energies of alpha parti- provided the initial velocity fo is given 
cles from a given source To the source ,n per sec and the range R m cm 
there arc added small amounts of ra- of air thus 
dioelements which emit alpha particles 

oi knomi energies The analyjser then t-f =» 1 03 X 

sorts out the pulses produced by the 

particles from the different sources, There is consequently a direct connec- 
and, by noting which of the record- tion, as might hue been expected, be- 
ing instruments respond, the unknown tween the velocity with which an alpha 
alpha-particle energies can be esti- particle is ejected from its source, and 
mated from those which are known the distance it can travel before losing 

7 19 In 1910, H Geiger, at that its ability to produce ionization in air 
time in Rutherford s laboratory m 7 20. The energy E of an alpha par- 
Manchester, England, made some tide, m Mev, is related to the velocity 

* The inass implied here is the ordinary or rest mass which may be used provided r does 
not approach the velocity of light (§ 3 to) Since the speeds of alpha particles expelled jn 
radioactive changes rarely, if ever, exceed one tenth of the speed of light, this condition u 
satisfied The modification necessary for particles of high velocity is given by equation (3 8; 



Nuclear Radiations 


bj' E = 2.08 X lO-'V, as seen above; 
hence it can be 6ho\^’n from equation 

(7.5) that 

El^' = 3.0972 or Eo = 2.l2R-i\ (7.6) 

where Eo is the initial enei'gy of the 
alpha particle in Mev, and R is its 
range in cm. of air. From equation 

(7.6) it is possible to obtain a moder- 
ately accurate estimate of the energj’’ 
of an alpha particle at its source, pro- 
vided the range has been measured. 
Thus the alpha particles from radium 
have a range of 3.29 cm. of air, and 
upon substituting this figure for R in 
equation (7.6), the initial energ)' is cal- 
culated to be 4.70 Mev, the directly 
raea.siircd value being 4.79 Mev. 

7.21. Actually, the Geiger formula 
and its equivalent equations (7.5) and 

(7.6) arc approximate, at best, and in 
any event they arc applicable only for 
alpha particles with ranges of from 3 to 
7 cm. of air. At lower ranges R is ap- 
pro.ximately proportional to and 
El'*, and at liighcr ranges to rj and El. 
As .1 result of experimental investiga- 
tions of the ranges and velocities, or 
energies, of alpha particles, and from 
theoretical considerations, cur\'es have 
l>een constructed which give the ener- 
gies of alpha particles as a function of 
their respective ranges. By means of 
thc.^ curves the energj' of an alpha 
particle of known range can be esti- 
mated quite accurately. Such curves 
have found many uses, some of which 
will be indicated in Chapter X 

The GEiGEn-KuTTALi. Rule 

7.22. It was pointed out in § 7.7 that 
the longest-lived mdioclcmcnts emit 
alpha particles with the shortest ranges, 
vhile the elements of short life c.xpel 
particles having long ranges. The 
pav^’ihility (hat a connection might 
exist Ixjtwecn tiie life |>criod of an 


155 

alpha-active element and the range of 
the particles emitted was suggested by 
Rutherford in 1907, and four years 
later, when sufficient data had become 
available, an approximate relationship 
was brought to light by H. Geiger and 
J. M. Nuttall. These workers showed 
that if the logarithm of the alpha-par- 
ticle range in air, i.e., log R, is plotted 
against the corresponding value of the 
logaritlun of the radioactive decay 
constant, i.e., log X, for a number 
of radioelements, an approximately 
straight line is obtained for each radio- 
active series. The Gdger-Nutiall rule, 
as it is called, is thus represented 
mathematically by the expression 

log X = A log R + B, (7.7) 

where X is the decay constant of the 
radioelement emitting alpha particles 
of range 72; the constant A. is the slope 
of the straight line, which is virtually 
the same for each series, but the values 
of B are different. 

7.23. Since the half life T is related 
to the decay constant X by equation 
(5.9), the term log X in the Geiger- 
Nuttall relationship may be replaced 
by log 0.693 — log T, i.e., by —0.159 
— log T; equation (7.7) then becomes 

-log T = A log 72 -f R', (7.8) 

•where B' is equal to B d- 0.159, but A 
has the same value as before. Conse- 
quently, the plot of log T against log R 
should also be a straight line for each 
radioactive series. 

7.24. Tlie various forms of the 
Geiger formula, namely, equations 
(7.4\ (7.5) and (7.6), show that there 
is a connection between the range 72 of 
an alpha particle and its initial velocity 
andenerg>'. It is thus possible to sub- 
stitute for 72 in ^nations (7.7) and 
(7.8), and to obtain expressions relat- 



156 Sourcebot^ on 

ing the decay constant or the half life , 
of the radioelement to either the initial 
energy or the initial velocity of the 
alpha particles For example, by com- 
bining equations (7 6) and (7 7) it la 
found that 

log X = ^ -A log Ea + B", (7 9) 

where A has the same value aa in the 
preceding equations but B" is a new 
constant \shich depends on the radio- 
active senes Thus, a straight Imo 
should be obtained if the logarithm of 
the decay constant of a radioelement is 
plotted against the loganthm of the 
energy of the emitted alpha particle 
Because of the limited applicability of , 
the Geiger rule relating the range to 
the energy, these plots usually show a 
slight curvature 

Theory op AnpHA-PARTicLB 
Emission 

7 26 In reporting their correlation 
between the life of a radioelement and | 
the range of the alpha particle emitted, 
Geiger and Nuttall wrote “The con- I 
nection between the penod and i 
the range is at present only empirical, 
but it may depend on some simple rela- 
tion which may ultimately be brought 
to light “ It 13 true that several years 
later a theoretical relation between the 
life of a radioelement and the energy of 
the alpha particle was developed but 
the approach was far from simple, as 
will soon be apparent 

7 26 In experiments on the scatter- 
ing of alpha particles, such as those de- 
scribed m § 4 7, it was found that even 
the fastest of such particles from radio- 
active sources, having an energy of 10 
Mev, are repelled by atomic nuclei 
How ever, the more energetic the parti- 
cle the more closely can it approach the 
nucleus before it is turned back This 
conclusion applies to all nuclei, mclud- 


Aiotme Energy Chap Vll 

iDg those of radioactne atoms A1 
though alpha particles are prevented 
by repulsion from entenng the nucleus 
from outside, it is an undoubted fact 
that radioactive nuclei emit alpha par- 
ticles, so they must be able to exist, at 
least for a short time, within such 
nuclei The interactions between a 
radioactive nucleus and an alpha par- 
ticle, outside and inside the nucleus 
can be represented pictonally by a 
potential energy curve such as that m 
Fig 7 4 The rising portion of the 



Fio 74 Potential energy curve (hypo- 
thetical) for interaction between an atomic 
nucleus and an alpha particle 

curve from A to B indicates increasing 
repulsion of an alpha particle as it ap- 
proaches the nucleus, on the other 
hand, the sharp fall from B to C, which 
IS essentially the region withm the nu- 
cleus, implies the existence of the alpha 
particle m this region 
7 27. Calculations have shown that 
the point B, at the maximum of the 
curve corresponds to an energy of 
about 25 Mev, for an element of high 
atomic number Hence, it may be con- 
cluded that an alpha particle with 
energy less than this amount will be re- 
pelled if it approaches the nucleus from 
outside, 1 e , from right to left of the 
diagram An alpha particle with en- 
ergy E, about 10 Mev, approaching the 
nucleus, as shown in Fig 7 4, will be 




Nuclear Radiations 


ttinicd back when it reaches a distance 
from die center of tlic nucleus corre- 
sponding to the point D. An energj' of 
at least 25 Mev would be necessarj' for i 
the alpha particle to reach the nucleus 
without suffering repulsion. 

7.28. Scientists often speak of the 
conditions represented by Fig. 7.4 as 
being due to a potential barrier, since 
something analogous to a barrier is 
preventing the entry of alpha particles 
into the nucleus. However, it must be 
clearly understood that the term ‘‘bar- 
rier” is u.sed in a figurative sense only; 
it is not meant to hnplj'’ the existence 
of a material barrier, but rather of re- 
pulsive forces which are equivalent to a 
barrier. It is important to appreciate 
this point, bec.ause the shape of the 
potential energy curve, and hence that 
of the figurative “barrier,” varies unth 
the nature of the particle approaching 
the nucleus, ^^^lcn the particle is a 
proton, for example, the “barrier” is 
much lower than for an alpha particle, 
and when it is a neutron, the “barrier” 
is virtually not existent. In other 
words, the force of repulsion between a 
nucleus and a proton is less than for an 
alpha particle, while there is essentially 
no repulsion between a nucleus and a 
neutron. 

7.29. So far there appc.ars to bo no 
objection to the foregoing discussion, 
but an\ore careful examination reveaks 
a difuculty. If .m alpha particle must 
have an energy equal to, or greater 
than, that corresponding to the maxi- 
mum point B of the potential energj' 
cuno, i.c., 2.5 Mev, to got into the 
tuwleus from outdde. then an alpha 
particle from the interior of the nucleus 
.should have at least the s.amo amount 
of energy* to escape. That i.s to .«ay, if a 
potential harrier prevents the access of 
alpha particle* from outside the nu- 
tlein, the satire barrier .diould prevent 
tic- e:nb ion of p.srtides from the inte- 


157 

rior. It is surprising, therefore, to find 
that alpha particles are produced from 
radioactive .sources udth energj’- as low 
as 4.3 IMev, and for no natural radio- 
element does the alpha-particle energj’’ 
exceed 10.6 ]\Iev. 

7.30. Classical mechanics provided 
no explanation of this state of affairs, 
but in 1928 the English physicist R. W. 
Gurney in collaboration with E. U. 
Condon of the United States, and the 
Russian-born G. Gamow independ- 
ently showed that the paradox could be 
resolved by means of the then newly- 
dermloped rvavc mechanics (§ 3.99). 
According to classical theory, an alpha 
particle inside the nucleus cannot sur- 
mount the barrier and escape if its 
energy is less than 25 Mev, but wave 
mechanics requires there should be a 
definite, if small, probability that such 
a particle from the interior udll be 
found outside the nucleus. In other 
words, there is a definite probability 
that the alpha particle will escape from 
the nucleus even when its energy is less 
than that of the top of the hypothetical 
barrier. If the energy of the particle is 
equal to, or exceeds, the value at the 
top of the barrier then the probability 
of escape amounts, of course, to a cer- 
tainty, according to both classical and 
wave-mechanical theories, 

7.31. By using the equations of wave 
mechanics, a complex expression can 
be derived for the probability that an 
alpha particle of given energj’’ will es- 
cape when it reaches the exterior sur- 
face of the nucleus. In general, it can 
be 6.aid that this probability is greater 
the larger the energj^ of the alpha par- 
ticle relative to the top of the barrier, 
and the smaller the “thicloiess” of the 
barrier at the point coiTesponding to 
the given energ}' v.alue. It c.an be seen 
from h ig. 7 ,4 that tlie higher the energy* 
the le.ss the thickne.^s of the barrier; 

I hence, both factors influencing the es- 



158 Sourcebooh on 

cape probabibty operate in the same 
direction It follows, therefore, that 
the greater the energy of the alpha , 
particle in a radioactive atom, the more ^ 
likely is it to be found outside the nu- 
cleus Tins IS the fundamental basis of I 
the fact that radioelements which dis- | 
integrate rapidly emit alpha partidcs , 
of high energy and long range, whereas 
the long-lived elements produce parti- 
cles of relatively low energy and short 
range (§ 7 19 et seq ) 

7 32 An approximate value of the 
frequency with which alpha particles 
reach the exterior surface of the nu- 
cleus can be obtained upon dividing 
the radius of the nucleus by tiie esti- 
mated speed of the alpha particle If 
this frequency, expressed as the num- 
ber per second, is multiplied by the 
probability of escape, the result will 
give the frequency with which alpha 
particles actually escape, this is equiv- 
alent to the radioactive decay constant 
X, m reciprocal-second (sec ”*) units 
It will be apparent from what has al- 
ready been stated that the value of X 
will, m general, be larger the greater 
the energy of the alpha particle By 
making a number of simphfying as- 
sumptions, the wave-mechanical treat- 
ment leads to a relationship between 
the decay constant X and the enei^ of 
the alpha particle which is somewhat 
srmxfar to the Geiger-^'httaff rufe in i 
the form of equation (7 9) It may be 
remarked m this connection, that m 
order to make the theoretical equations 
fit the experimental results, the effec- 
tive radius of the nucleus must be 
taken as approximately equal to 1 5 X 
cm , where A is the atomic 
weight (mass number) of the radio- 
element (see § 4 19) 

7 33 The theory outlined above, al- 
though moderately satisfactory, can- 
not yet be regard^ as complete One 
of the weaknesses is the assumption 


Alomtc Energy Chap Vll 

that the nucleus contains alpha parti- 
cles, which is contrary to the modem 
view that atomic nuclei consist of neu- 
trons and protons only But since a 
combination of two neutrons and two 
protoiw, which is essentially an alpha 
particle, has been shown to be excep 
tionally stable (§ 4 41), it is probable 
that the particle may exist in the 
nucleus for short intervals of time 
Improvements of the wave-mechamcal 
treatment, based on the transient for- 
mation of alpha particles prior to their 
ejection, must await further develop 
ments in nuclear theory (| 15 91) 

7 34 In view of the probability of 
the escape of alpha particles from ra- 
dioactive nuclei even when their energy 
18 insufficient to surmount the barner, 
It might be argued that there should be 
a similar probability that alpha parti- 
cles from outside with the same amount 
of energy should be able to reach the 
nucleus without being repelled This 
argument is completely justifiable, and 
there is no doubt that such penetration 
does take place m the bombardment 
processes which cause nuclear rear- 
rangements (Chapter IX) 

7 36. It 13 instructive, however, to 
calculate the probability of an alpha 
particle escaping from, and of return- 
ing to, an atomic nucleus The radius 
of a nucleus is about 10"^* cm , and the 
speed of an alpha particle moving as 
the nucleus is perhaps 10* cm per sec 
Consequently, as a rough approxima- 
tion, an alpha particle will find itself at 
the extenor surface of the nucleus 10*/ 
10~“, 1 e , 10^\ times per second Upon 
I multiplying this frequency by the es- 
j cape probability, the result will give 
Uie decay constant X, in sec umts, as 
seen above The actual \alues of X 
vary from roughly 10^ sec for tho- 
rium C' to I0~** sec for thorium, 
hence, the probability of escape ranges 
from 10““ to 10~** This means that 



Nuclear Radiations 


even with the verj” short-lived radio- 
element thorium C', an alpha particle 
in the nucleus, vdth an energj’- of about 
9 Mev, makes on the average lO’'’ at- 
tempts before it succeeds in escaping. 
For thorium, in only one attempt in 
does the alpha particle, of energj* 
about 4.3 Mev, leave the nucleus. 

7.36. It is because of the very large 
number of escape attempts made by 
the alpha particle, i.e., the large num- 
ber of times it reaches the exterior 
surface of the nucleus, namely, about 
10-® times per second, that radioac- 
tivity is an observable phenomenon. 
When a nucleus is bombarded by alpha 
particles from outside, however, the 
number of attempts at entry is verj' 
much less, and hence the effects are 
not so marked, although the probabil- 
ity of entering the nucleus is the same 
n.s the probability of escaping, for the 
same cnerg)’- value. 

ALPHA-PAHTicnn Spectha 

7.37. Although it has been assumed, 
so far, that all the alpha particles from 
a given source have virtually the same 
range and energy, this is not strictly 
the case. It is generally true that a 
large proportion, if not all, the particles 
have identical energies, but in some 
instance.? particles with different ener- 
gies have been detected.* The pres- 
ence of a very small number of particles 
of exceptionally high energj' was ob- 
served by E. Rutherford and A. B. 
Wood in 1916 in the radiations from 
thorium .active-deposit, probabl}* orig- 
'mating from thorium C'; three years 
later Ibitherford noted that similar 
losrg-rango particles were emitted from 
mdium active-deposit. It was not until 
1930. however, that S. RosenbUun, in 
1' ranee, proved definitely by means of 
.a magnetic S]>ectrograph, “^similar to 


159 

that described in §7.15, that the alpha 
particles from thorium C, all of which 
had been thought to have the same 
energy, actually consist of a number 
of groups of particles, with slightly 
different energies. 

7.38. Since that time, several physi- 
cists have made detailed studies of 
the distribution of energy among the 
alpha particles from a number of radio- 
elements. In a few cases, the particles 
were found to be monoenergetic, all 
having essentially the same energy, 
but in many instances there was a 
definite alpha-particle spectrum, con- 
sisting of two or more discrete groups 
— as many as thirteen for radium C' 
and polonium — of different energies. 
A simple example is provided by tho- 
rium C which emits five groups of 
alpha particles whose energies are 6.084, 
6.044, 5.762, 5.620 and 5.601 Mev, 
respectively; the first group constitutes 
27.2 per cent and the second 69.8 per 
cent, so that these two together make 
up 97 per cent of the total. 

7.39. The occurrence of alpha-parti- 
cle spectra can be accounted for by the 
existence of definite energy levels in 
atomic nuclei, as stated in §4.77, In a 
radioactive disintegration the nucleus 
of the parent element, thorium C, for 
example, is almost invariably in its 
lowest energy state, but the nucleus 
of the daughter element, thorium C", 
formed as a result of the emission of 
an alpha particle, may be either in its 
lowest (ground) state or in any one of 
four higher (excited) levels. The en- 
erg}' of the alpha particle thus depends 
on the energy levels of the parent and 
daughter nuclei involved in the dis- 
integration. Tlie five groups of parti- 
cles obsen'cd for the transition from 
thorium C to thorium C" are inter- 
preted in this manner, as shovm in 


^ of fkc alpha particles froi 



ICO 


Soured}ooK on Atomic Energy Chap VII 


Fig 7 5 and the alpha particle spectra 
of other radioelements can be explained 
similarly The transition to the second 
level of thorium C" is evidentlj the 
most probable, since the largest pro- 
portion of alpha particles have the 
energy corresponding to this particular 
change 

740 When the nucleus of the daugh- 
ter element in a radioactive transition 
IS formed m an excited state it can 
change to a lo^er energy state by the 
emission of radiation This appears 
as gamma rays as will be explained 






Fiq 7 5 Explanation of alpha particle 
spectrum from thorium C 


m §7 82 The fact that there is an 
almost exact correlation between the 
energies of the groups of alpha parti- 
cles and the energies of the gamma 
rays is strong confirmation for the fore- 
going explanation based on nuclear 
energy levels 

7 41 In two or three instances, such 
as, thorium C' and radium C', a very 
small proportion of highly energetic 
alpha particles are due to the par- 
ent nucleus bemg in an excited en 
ergy state, while the daughter element 
thorium D and radium D, respectnely, 
is m its lowest (groimd) level The 
circumstances are here some^^hat ex- 
ceptional An appreciable amount of 
thonum C' is formed m an excited state 
upon decay of its parent, but the prod- 
uct has such an extremely short half 
life — ^3 X 10“^ sec — that about on© 
nucleus m a million ^vlll disintegrate 
to thonum D straight from the excited 
state before it has an opportunity to 
emit the excess energy as gamma radia- 
tion Similar considerations apply to 
the disintegration of radium C', which 
has a half bfe of 1 5 X 10^ sec 


THE PROPERTIES OF BETA RADIATIONS 


Beta-Particle Energies 
7 42 It wll be recalled that whereas 
alpha psrtjrJos 3Te positively ehargsd 
and have a mass of about 4 on the 
atomic weight scale, beta rays con- 
sist of electrons so that they are 
■\cry hght, negatively charged parti 
cles Apart from these distinctions 
there is a highly important respect 
m which alpha and beta particles dif- 
fer, to w hich attention must be called 
at the outset It w as seen in the pre- 
ceding section that alpha particles are 
either monoenergetic or else there is a 
spectrum made up of a limited number 
of discrete groups having definite en- 


ergies, beta particles, on the other 
hand, do not behave in this manner 
7 43 In 1900 H Becguerel noted, 
from their behavior in a magnetic field, 
that the deviable radiations, i e beta 
rays, were complex, forming a contmu- 
ous ^stribution of velocities, and hence 
energies But during the early years of 
Uie present century there was a differ- 
ence of opinion among workers in the 
field of radioactivitj some thought the 
beta particles from a given source had 
a wide range of energies, while others 
were of the opinion that they were 
essentially monoenergetic The latter 
view appeared to find support m the 



Nuclear liadiadone 


discovery, made by 0. von Baeyer, 
0. Haim and L. Meitner in Germany, 
in tlie years between 1910 and 1912, 
of the existence of homogeneous (mono- 
encrgetic) groups of electrons in beta 
rays. But doubt was cast on their sig- 
nificance when, in 1914, J. Chadwick 
found that they constituted a small 
fraciion only of the total beta particle 
crai.ssion. The opinion was therefore 
expressed that the main portion of the 
electrons emitted by a radioactive ele- 
ment, which showed a continuous dis- 
tribution of energj’-, were the tivie dis- 
integration beta particles, and that the 
weaker monoenergetic groups were due 
to a sccondarj' effect. A theorj’^ of the 
origin of these secondarj' electrons w'as 
proposed by E. Rutherford in 1914, 
and supported by Lise Meitner in 1922, 
after she and 0. Hahn had shown that 
similar groups of monoenergetic elec- 
tron.s were sometimes found associated 
with alplxa-particle di.sintegration. The 
nature of these secondarj’- electrons, 
which arc associated wdth the emission 
of gamma rays, tvill be considered in 
^ 7.8G. 

7.44. Two main methods have been 
used for the study of the distriljution 
of cnerg}' among the beta particles 
from a given radioactive source. The 
firet makes use of the 180° (or semi- 
circular) magnetic spectrograph which 
is quite similar in principle to that 
described in §7.1.5 for the determina- 
tion of the velocities of alpha particles. 
The best fonn of apparatus is that in 
winch a Geiger counter is placed in a 
fixed po.«ition, such as P in Fig. 7,3. 
1 he magnetic field H is then varied, and 
the mimhers of beta p.arlicles reaching 
onuntcr in a given time for the 
diucrx.'nt values of // are recorded. 
I' ronx If and the fixed radiu.'? r of the 
femicirrular path taken by the beta 
particles, the velocity v of the latter 
can be calculated hy means of equa- 


161 

tion (7.2); each value of H thus cor- 
responds to a definite velocity. In this 
way, the relative numbers of beta par- 
ticles having various velocities can be 
determined. 

7.45. Since the speeds of beta parti- 

cles as they emerge from radioactive 
sources approach the velocity of light, 
allowance must be made in equation 
(7.2) for the relativistic increase of 
mass. If, as required by equatio n (3.8), 
m is replaced by mo/ Vl — where 

mo is the rest mass of the electron, v is 
the initial speed of the emitted beta 
particle, and c is the velocity of light, 
equation (7.2) becomes 

—Hr Vl - v^/(?, (7,10) 

mo 

which is the form to be employed in the 
present instance. Further, the (ki- 
netic) energj' of the beta particle is no 
longer given merely by ^me-, as is 
the case for the comparatively slow- 
moving alpha particles, but by 

E = mcri ( (7,11) 

VV l - ) 

The calculations of the energy from 
the magnetic field and cunmture of 
the path are thus somew'hat more com- 
plicated, but they can be made wdthout 
too much difficulty by means of equa- 
tions (7.10) and (7.11). 

7.46. The second method wdiich has 
been employed in the determination of 
beta-particle energies makes use of 
what is known as the viacjnetic-lens 
spectrometer; the principle involved is 
essentially the same as that used for 
focusing in the electron microscope, 
and it is for this reason that the name 
magnetic lens or electron Ions has been 
applied. In outline, the apparatus con- 
sists of a cylinder (Fig. 7.6) around 



162 


Sourceboc^ on Atomic Energy Chay YU 

which IS wound a coil (solenoid) of with different energies, can be deter* 
copper wire, when a current is passed mined 

through this wre a magnetic field is 7.48 The results obtained with a 
produced in the cylinder, its direction variety of different beta-active sources, 
being parallel to the axis The radio- both natural and artificial (Chapter 
activesourceisplacedatonecndofthc IX), arc all of the same type Apart 
cylinder at 5, while at the other end, from the few groups of monoenergetic 
at C, there is a suitable Geiger-MuUer electrons sometimes observed, the over- 
counter with a thm wall which the whelming proportion of the beta par- 
beta particles can penetrate By means ticl^ from any source exhibit a con- 
of the baffles shown at the left, the tmuous distnbution of energy, i e , a 
particles leaving the source 5 in a beta-particle spectrum, from almost 
definite direction are permitted to en- zero iip to a definite maximum, the 



tNEner 

ter the longitudmal magnetic field, this pio 7 7 General form of distribution of 
field constrains them to follow a helical enemies among beta particles (beta particle 
(spiral) path, a projection of which is spectrum) 

shown by the dotted lines m Fig 7 6 

7 47. By suitably adjusting the cur- latter varying with the source If the 
rent m the solenoid, and thus changing relative number of particles possessmg 
the magnetic field, beta particles from a particular energy is plotted against 
S can be "focused" so that they per- the energy, the points invariably fall 
form a single turn of the helix and just on a curve such as that depicted in 
reach the wall of the counter For a Fig 7 7 The maximum energy, ob- 
grven vmhe ai'^ftemagneAc rfeitf, omV (Jimnai’Cry-asAor^exifrap^ xs-imA'- 
those beta particles which have a par- cated by The maximum veloc- 

ticular velocity will reach the counter ities of beta particles range from about 
The velocity can be calculated from 25 to 99 per cent of the speed of light, 
the magnetic field and the dimensions the corresponding values of £bi« vary 
of the apparatus As a general rule, from 0 025 to 3 15 Mev, most of them 
however, the instrument is standard- being m the vicinity of 1 Mev 
izcd by means of electrons of known 

speed, and the velocity can then be Neutrino Theory 

deteimmed directly from the current 7 49 The problem of the contmu- 
flowing through the solenoid In this ous distribution of energy among beta 
manner, the relative numbers of beta particles concerned physicists for a 
particles, as detected by the counter, number of years It seemed highly 
mth different velocities, and hence improbable that it could be due to the 



Nuclear Radiations 


existence of a continuous series of en- 
erg}' levels in either parent or daughter 
elements, since all the evidence points 
to the presence of a few discrete levels 
only. If the variation in energy among 
the beta particles were due to transi- 
tions between different energj’’ states, 
then there should be a continuous dis- 
tribution of gamma ray energies to 
correspond to that for the beta parti- 
cles, but no such phenomena have been 
observed. A radioactive beta transi- 
tion, like an alpha change, must be ac- 
companied by a definite energj’- change, 
and there is reason for belie\nng that 
this is the maximum beta-particle en- 
ergj', iSnisi. It was seen in § 5.60 that 
thorium C imdergocs branched disinte- 
gration, but the two branches rejoin at 
thorium D. The energy difference by 
<hc path thorium C — + thorium C — > 
thorium D should be exactly the same 
as that for the alternative path tho- 
rium C — >■ thorium C" — > thorium D. 


163 

integration processes, but this view 
could not be entertained seriously. Ul- 
timately, in 1931, a way out of the 
difficulty was indicated by W. Pauli 
(see §4.64), and this was elaborated 
by the famous Italian-born physicist 
E. Eermi in 1934. There is little doubt 
that the atomic nucleus does not con- 
tain free electrons, but only neutrons 
and protons (§4.35); hence, the elec- 
trons which were emitted as beta rays 
by radioactive nuclei must result from 
the spontaneous conversion of a neu- 
tron into a proton and an electron. 
Pauli suggested that this process was 
accompanied by the emission of an- 
other particle, now called a neidrino*) 
this was assumed to be electrically 
neutral and to have a very small rest 
mass, small even compared to that 
of the electron. Thus, the creation of 
an electron in the nucleus, prior to its 
emission as a beta particle, would be 
represented by the process 

(7.12) 


neutron — » proton -f- electron -f neutrino 
mass 110 0 

charge 0 -b — 0 


Careful measurements shoAv that this 
is tnie only if in the transitions tho- 
rium C — ‘ thorivim C' and thorium C" 
— ♦ thorium D the beta particle ener- 
gies are those corresponding to Emax 
in each instance. 

7.50. The problem is then: What 
happoms to the additional energy' in 
the case of the great majority of beta 
particles whose energj' is less than the 
maximum? The situation was so des- 
perate that some eminent physicists 
Fupgt-sferl that the law of conscrx'ation 
of enorgv’ might not hold in beta-dis- 


7.51. It win be seen that the two 
sides of the equation balance with re- 
spect to both mass — given to the near- 
est integer — and charge. In a beta- 
decay process, the proton remains in 
the nucleus, but the electron and the 
neutrino are ejected. In order to ac- 
count for the continuous distribution 
of energy among beta particles Pauli 
supposed that the total available 
energ}', equal to Emax, was divided be- 
tween the electron (beta particle) and 
the neutrino. Thus the difference in 
energy between and the actual 


tlic ItalLin, mo.aning a 'Vmal! neutral one.’’ The neutrino concept was proposed bv 
^ Scnnnnr in Theoretical Phy.cics held in the University of Michigan in the sum- 
Jyt . -nn, name neutron" was first used for the particle, but after the discoverv- of 

(§2.112), the terra neutrino was adopted, 
..pjesn riUy hy K. Pcrnii. ‘ ’ 



164 Sourcebook on 

value for any given beta particle would 
be carried off by the accompanying 
neutrino 

7 52 By applying the methods of 
wave mechanics to the neutrino hy- 
pothesis, as just outlined, Fermi was 
able to derive a complicated equation 
giving the probabihtj of the emission 
from a radioactive nucleus of a beta 
particle with energy in the vicinity 
of any specified value The plot of 
this probability function against tho 
corresponding energy value should ha\ e 
gi\ en a curve similar to that m Fig 7 7 , 
although it was of the correct form, 
the agreement with experiment did not 
appear to be too good However, be- 
cause of the lack of reliable experi- 
mental data at the time, the earlier 
tests of the theory were not conclusive 

7 63 More recent work, particularlj 
with artificial beta-active radioelc- 
ments of fairly low atomic weights, , 
has given results which provide sup- 
port for the neutrino theory The tests ' 
have been facilitated b} the use of a 
method of plotting suggested m 1936 
by F N D Kune J R Richardson 
and H C Paxton in the United States 
They showed that the Ftrmi probabil- 
ity equation could be rearranged to 
take the form 

K iN/r)y^ = C - (F -hi), (7 13) 

where N is the number of beta parti- 
cles of momentum (or energy) lying 
avithin a certain narrow range, / is a 
complex function of the corresponding 
beta-particle energy E as worked out 
by Fermi, and K and C are constants 
The energy E of the beta particle is 
here expressed in umts of woc*, where 
Wo is the rest mass of the electron 
and € IS the a elocity of light Accord- 
ing to equation (7 13), the plot of 


AUnrnc Energy Chap 1 U 

against E + 1, often referred 
to in the scientific literature as a Kune 
plot,* should be a straight line if the 
Fermi neutrino theory is to be sub- 
stantiated Where reliable data are 
available it appears that they do give 
a straight line, except perhaps for very 
low energj values 

7 64 Apart from the fact that the 
neutrino concept has proved useful in 
solving a difficult problem in nuclear 
science, it may be wondered if there 
is any direct experimental evadence for 
the existence of such a particle In 
view of Its very small rest mass, prob- 
ably not more than a few hundredths 
of the mass of an electron, and the 
absence of electric charge, the neutnno 
would be expected to pass readily 
through matter and hence would be 
difficult to detect It ma\ bo men- 
tioned m this connection that when 
in 1927 C D Elhs and \V A Wooster, 
m Rutherford’s laboratory, determined 
the heat gi\ en out by the beta parti- 
cles fiom radium E, the value corre- 
sponded to the average cnergj, and 
not to tho maximum energy, of the 
particles This result implies that if, 
as now supposed, the disintegration 
energy is shared betw een beta particles 
and neutrinos, the former ga\ e tip all 
their energy, while the latter escaped 
from the apparatus wath virtually no 
Toss of energy 

7 65 One a\ay in which direct evi- 
dence for the neutnno might be ob- 
tained IS by studying the recoil of the 
daughter nucleus in a beta disintegra- 
tion A number of investigations of 
this kind have been made, and al- 
though it cannot be claimed that the 
results are decisive, at least it can be 
said that there is no evidence which 
makes the existence of the neutnno 
improbable 


Also sometimes called a Fermt plat 



NticJcar Radiaiions 


7.66, In some respects a verj’- con- 
vincing argument that beta-particle 
emission must be accompanied by an- 
other particle is provided by a con- 
sideration of the spins of the neutron, 
proton and electron. It was seen in 
§ 4.79 that the spin quantum numbers 
of these particles are either -f or 
- 14, and since these numbers must bal- 
ance on both sides of equation (7.12), 
for the conversion of a neutron into a 
proton and an electron, it follows that 
the process must involve another parti- 
cle whose spin is also probably 

or -’• 2 . 

AnsonpTioN akd Range of 
Beta Pahticles 

7.67. Cloud chamber photographs of 
beta particles (Fig. 6.8) are much less 
distinct than those produced by alpha 
particles, since the small mass of the 
former leads to a much smaller specific 
ionization in their path. Further, it is 
found that the tracks are not straight 
lines, bec.ausc the beta particles un- 
dergo frocpient scattering. If the t.otal 
length of the track of a beta particle 
could bo mc.asurcd in air it would prob- 
ably be found to be several meters, as 
{'ompared with a few centimeters for 
alpha particles. But such measure- 
ments are difiicult, and so the range 
of a beta particle is usually defined 
in term.s of tlic equivalent thickness 
(I 7.10), expressed in mg./cm." or in 
gram/cm.-, of an absorber, usually 
aluminum. 

_ 7,68. As the result of a series of 
circumstance.?, fairly good and repro- 
tiucible results can be obtained in spite 
of the undoubted vari.ations in actual 
range corrc-sponding to the distribu- 
te, .m of energy among the beta parti- 
cles. It is an interesting and useful 
fad tliat for light elements, at least, 
the^ah.^onttion thickness in mg./cm.” 
p almost independent of the nature of 


165 

the absorber. Hence, if a radiation 
detector, such as a Geiger counter, is 
kno\vn to have a mica window with a 
thickness of 5 mg./cm.-, the equivalent 
value for aluminum would be approx- 
imately the same. It is thus possible 
to make allowance for the absorption 
by the wdndow when necessary. 

7.69. The absorption of beta parti- 
cles can be studied by placing the 
radioactive source near the thin wmll 
of a suitable counter, and then record- 
ing the counting rate with various 
thicloiesses of absorbing material in- 
serted between the source and the 
counter. If a monoenergetic stream of 
electrons is used in such an experi- 
ment, it is found that the absorption 
curve showing the number of particles 
passing through the absorber falls off 
steadily, in a roughly linear manner, 
as the absorber thiclcness is increased. 
Tliis is quite different from the be- 
haxdor of alpha particles, where, as 
indicated in Fig. 7.2, the counting rate 
remains almost constant until near the 
end of the range, when it falls quite 
sharply to zero. The reason why elec- 
trons act differently in this respect is 
parti}'- because they lose energy by 
conversion into radiation, in addition 
to that used up in the formation of 
ion-pairs, but largely because they un- 
dergo ver}'- marked scattering, with 
frequent changes in direction, espe- 
cially when passing through a solid 
absorber. 

7.60. Since beta rays are not mono- 
energetic in nature, but consist of par- 
ticles with a vide range of energies, 
the absorption curves are not linear 
but are more complicated in character. 
Because of .a curious combination of 
factors, it so happens that if a graph 
is drawm of the lotjariihm of the count- 
ing rate for various absorber thick- 
nesses against the thickness of ab- 
sorber, the result is an approximately 



166 

straight Ime, as depicted in Fig 
It lull be noted that beyond a certain 
absorber thickness, the counting rate 
no longer decreases but remains al- 
most constant This residual activity 
IS due to the presence of the hi^ly 
penetrating braking radiation (Brems- 
strahlung), analogous to continuous 
X-rays (§4 75), resulting from the 
rapid deceleration of the fast-moving 
beta particles in the absorbing medium 
The extent of the formation of this 



Fxo 7 8 Absorption of beta particles in 
matter 

radiation increases with the atomic 
number of the absorber If gamma 
radiation accompanies the beta rajs, 
as IS often the case, the curve for the 
residual counting rate is considerably 
higher, smce it is now due to the 
gamma rays m addition to the Brems- 
strahlung 

7 61 From a cursory examination 
of Fig 7 8, it might be concluded that 
the falling portion of the curve could 
be extrapolated to zero counting rate, 
m Fig 7 2, to give the effective 
range of beta particles m the absorber, 


Chap VI! 
appreciable amounts of gamma radia- 
tion are present A proposal for over- 
coming this difficulty, made by the 
English physicist N Feather, m 1938, 
has been ividely adopted The absorp- 
tion curves of the beta particles from 
the ^ven sources are compared with 
the published data for radium E, the 
latter ^bstance emits beta particles 
free from gamma rays and their max- 
imum range is known to be equivalent 
to 476 mg /cm ® of aluminum Conse- 
quently by using the radium E as a 
standard, the maximum range of the 
beta particles under examination, m 
terms of mg /cm * of aluminum, can be 
derived \vith the aid of a Feather plot, 
as tt IS caVed 

7 62 The importance of the maxi- 
mum range as obtained m this 
manner, is that it is a characteristic 
property which can be used to identify 
the source and to determine the maxi- 
mum energy Em»* of the beta particles 
A number of measurements have been 
made of both the maximum energy, 
using some form of magnetic spec- 
trometer, as described in § 7 44 et seg , 
and the maximum ranges of beta parti- 
cles from a variety of sources, from 
them accurate data have been obtained 
from which a curve of Ena* (m Mev) 
against (mmg /cm *or gram/cm ^ 
of aluminum) has been plotted Hence, 
if a value of Rma* for beta particles 
from a given source is obtained by 
Feather s method, the corresponding 
maximum energy Em»x can immedi- 
ately be read off from the curve As 
a less accurate alternative, use may be 
made of the relationship 


Sourcebook on Atomic Energy 
78 


Emax (Mev) =* 1 85Bni„ (g /cm *) + 0 245, (7 14) 


apart from the extraneous radiation which applies when is greater 

The results obtained in this way are, than 0 3 gram/cm *, i e , 300 mg /cm 
however, very unreliable, especially if and Em** exceeds 0 8 Mev 




Nuclear Radiations 


167 


Decay Constain't and Maximtoi 
Energy of Beta Particles 

7.63. Tn seeking for a relationship 
betu-een the radioactive decay con- 
stant X of beta-emitting radioelements 
and the maximum energy Emux of the 
particles, analogous to the Geiger- 
Kuttall laiv for alpha decay (§ 7.22), 
the Canadian physicist B. W. Sargent 
found in 1933 that if the log X values 
for various radioelements were plotted 
against the corresponding values of 



Jo? 

Inn. 7.0. Saigcnt curves sliowing rcla- 
tionsliip licUvco!v decay constants and m.ax- 
innim beta-particle energies. 

most of the points fell on two 
st might lino-s. Although these lines, 
known .ns Sargoit curves, are approx- 
imately p.nrallol (Fig. 7.9), the ele- 
ments cm each cun'c do not necessarily 
belong to the same radioactive series, 
as in the case of the analogous Geiger- 
X’uttall plots. 

7.G4, .Vn interpretation of the Sar- 
gent diagram was provided bj' the 
I'vnni theory of beta decay based on 
the neutrino concept (§7.50). Accord- 


ing to this theorj’', the deca 3 f constant 
X should be approximatelj^ related to 
the maximum energy Emax by the 
equation 

X = (7.15) 

so that, upon taking logarithms, 

log X = log A -f 5 log Dmnx. 

For all beta emitters to which the 
same k applies, the plot of log X against 
log E,„tix should be a straight line with 
a slope of 5, as is approximately^ true 
for the Sargent plots The value of 
fc, which determines the position of 
the line on the diagram, depends on 
whether the radioactive process in- 
volves a “permitted” or “forbidden” 
nuclear transition (§ 4.55). 

7.66. Theoretical considerations in- 
dicate that the probability of a nuclear 
transition, in general, is dependent 
largel}’^ on the difference in the nuclear 
spins (§ 4.79) of the initial and final 
states.* For a "permitted” transition, 
that is, for one of high probability, 
the change in the nuclear spin quantum 
number is zero or perhaps unity. For 
larger differences in the nuclear spins 
the transition probabilitj'- becomes 
smaller and the transitions are increas- 
ingl.v “forbidden.” A scries of stages 
or degrees of increasing “forbidden- 
ness” are thus to be expected. The 
upper (first) S.argcnt curve evidentlj’- 
corresponds to allowed transitions, and 
the lower (second) curve to forbidden 
transitions of, at least, the first degree. 
In the latter case log k should be ap- 
proximatelj'' 2 units less than in the 
former, and this is in general agreement 
with the results plotted in Fig. 7.9. 

7.66. In recent j'ears there have be- 


, * ."-'‘vv-tni'rhnnical projKrty of tlic nucleus, called its parilij, is also important; tins is 
fin the resultant orbital angular momentum of the nudeons. 




168 SourcehodL on Atormc Energy Chap YII 

come available a considerable number curve lying m betv.een the latter ishich 
of beta-emitting radioelements 'tthich actually represents forbidden transi 
do not occur m nature, from an exam- tions of the first degree In this case, 
ination of these substances it appears the loivcr Sargent curve of Fig 7 9 cor 
that there are several other Sargent responds to transitions of the second 
curves, representing increasingly for- degree of forbiddenness The subject 
bidden transitions below the Ino is still in a state of development, and 
curves for the natural radioactive ele- there is little doubt that its study will 
ments In the opinion of N Feather ultimately contnbute to a fuller under 
expressed m 1948, there is possibly a standing of nuclear structure 

THE PROPERTirS OF GAMMA RADIATION 


Gamma Ray Interaction 
WITH Matter 

7 67 As recorded in § 2 104, gamma 
rays are electromagnetic radiations sim- 
ilar to Xra>« but of shorter nave 
length Actually it is not possible as 
far as their behavior is concerned, to 
distinguish between the longest gamma 
rays and the 5ho*-tcst X-rays, but it is 
usual to employ the term gamma rajs 
when the radiations originate within 
the nucleus and X rays when they 
are formed outside It was seen m 
§ 4 71 that characteristic X rays result 
from transitions between electronic en- 
ergy levels, gamma rays on the other 
hand, are associated with transitions 
between nuclear energy levels But 
once the energv is liberated the prop- 
erties of the resulting radiation arc 
determined by the frequency or wa\e 
length or in other words by the mag- 
nitude of the energy quantum In this 
respect gamma rays and X-rajs are 
\ ery similar Gamma rays accompany 
manj, if not all radioactive changes 
irrespectne of whether alpha or beta 
particles are emitted But, because 
alpha particles ha\ e a discrete ener^ 
spectrum, the study of alpha disinte- 
grations accompanied by gamma rays 
has thrown much light on the nature 
of the latter radiation 

7 68 Gamma raj s, like X-rays, are 


highly penetrating, the effective range 
depends on the energj, but it might 
require several centimeters of metal to 
reduce the intensity of gamma radia- 
tion to such an extent that it becomes 
difficult to detect In their passage 
through matter gamma rays lose their 
energy, and hence are absorbed in 
several ways, three being important 
enough to require consideration here 
The first, which is most significant for 
gamma rays of low energy, and for ab- 
sorbers of high atomic weight, is the 
photoelectric effect (§ 2 48), whereby 
electrons ore ejected from atoms of 
molecules encountered bj the radia- 
tion If E IS the energy of a gamma 
raj photon (§ 3 34), then m a photo- 
electric encounter an amount P, equal 
to the binding energy of the electron 
in the atom -will be required to remove 
the electron, and the whole of the re- 
mainder E — P IS earned off by the 
electron in the form of kinetic energy 
7 69 The second factor contributing 
to the absorption of gamma ra>s is 
the Co7npi(m effect (§3 35), this phys 
a major role when the absorber is a 
material of low atomic weight, and 
the energy of the radiation is neither 
too high nor too low Nevertheless, 
mcrease of the atomic weight of the 
absotber increases the extent of ab- 
sorption caused by the Compton effect 



Nuclear Radiations 


Wicn a gamma-ray photon collides 
with a free or loosely-bound electron, 
the latter removes some, but not all, 
of tie energj" of the radiation. The 
actual loss of energy depends on the 
scattering angle of the gamma rays, 
i.e., on the angle betAveen the direction 
of ll.o ra.vs before and after collision 
with the electron. In any event, as a 
result of a series of Compton encoun- 
ter.s, in passing througli an appreciable 
thickness of ab.sorber, the energy of the 
gamma rays may be so gr('atl}' dimin- 
bhed that they are no longer detect- 
able. 

7.70. For gamma raj's of high en- 
ergy the photoelectric and Compton 
oiTccts are not .so important for their 
absorption, especially in elements of | 
high atomic weight, as is the third 
factor, the fonnation of positron-elec- 
tron pairs (§ 2.71). A.s shown in Chap- 
ter ill, the process requires a minimum 
energy of 1.02 hlev, and hence it can 
have no influence on gamma radia- 
tions with less than this energy. The 
effect increa.sos rapidly, however, as 
the energy of the gamma-ray photon 
exceeds the minimum value. The prob- 
rddlity of pair formation increases with 
the square of the atomic mimber of the 
c.bsovher; this ex'plains why gamma 
my.s from thorium C", v.'ith an energy 
0 ! 2.G2 Jtfev, readily pr.oduce ])ositron- 
clecfron pairs when they pass tlirough 
lead. For absorbers of high atomic 
Vi’ciglu. and g-.imma rays of high cn- 
erg\', pair-prorhiction is the main cause 
of the energy loss. 

7.71. .Vs a result of the interactions 
leading to the photoelectric effect and 
o-’’ pair production, the gamma-ray 
photon loses the whole of its energy 
and cea<^o.s to eccist. In a Compton en- 
c-ninier. on the other liand. the photon 
ts di'privetl of n part only of its energy, 

tnentioned jibove; nevertheless, a 
-v proportion is transferred to the re- 


169 

coil electron (§ 3.35). Consequently, 
for each interaction between a gamma- 
raj’’ photon and matter, the result is 
either the ejection of an electron or the 
formation of a positron-electron pair 
carrj'ing a considerable amount of en- 
ergy. It is the ionization (§ 6.5) caused 
by these secondary electrons, produced 
in the gas or ejected from the walls of 
the counter, which provides a means 
for the detection of gamma rays, as 
described in Chapter 6. 

Absorption of Ga.mma Rays 

7.72. The .absorpt ion of gamma rays 
is studied in a manner similar to that 
described for beta particles (§ 7.59), 
except that the greater penetrating 
power rcv[uires the use of a heavy metal 
of high utoniic weight, such as lead, 
in place of aluminum, as absorber. For 
homogeneous gamma rays, consisting 
of radiations of a single frequency, or 
wave length, the plot of the logarithm 
of the counting rate (or intensitj’) 
against the thickness of the absorber 
is stnctly linear. In mathematical lan- 
guage, this means that the intensity 
of the radiation falls off exponentially 
with the thickness of the absorber, so 
that if lo is the intensity (or counting 
rate) of gamma rays from a given 
source wlion no absorber is used, and I 
is the intensity after passing through 
a thickness of x cm. of absorber, then 

I = (7.16) 

where c is the base of natural loga- 
rithm.?, and fi is a characteristic pro]>- 
erty of the absorber, known as its ab- 
sorption coefficient for the given gamma 
rays. The value of the absorption co- 
efficient varies with the cnergx'’ of the 
radiation, and it may be used, as e.x- 
plained below, to derive the gamma- 
ray energx'. 

7.73. If the radiation consists of sev- 



103 Sourcdmk on Atomic Energy Chap > /j 

come available a considerable number curve lying m between the latter which 
of beta emitting radioelemcnts which actually represents forbidden transi 
do not occur in nature from an exam- tions of the first degree In this case 
mation of these substances it appeara the lower Sargent curve of Fig 7 9 cor 
that there arc several other Sargent responds to transitions of the second 
curves, representing increasingly for- degree of forbiddenness The subject 
bidden transitions bclou the two is still in a state of development and 
curves for the natural radioactive ele- there is little doubt that its study will 
ments In the opinion of N Feather ultimately contnbute to a fuller under 
expressed m 1948 there is possibly a standing of nuclear structure 

THE properties OP GAMMA RADIATION 

Gamma Rai Interactiom highly penetrating, the effective range 

WITH Matter depends on the energy, but it might 

7 67 As recorded in § 2 104 gamma require several centimeters of metal to 
raysareelectromagneticradiationssim reduce the intensity of gamma radia- 
ilar to X-rays but of shorter wave tion to such an extent that it becomes 
length Actually it is not possible, as difficult to detect In their passage 
far as their behavior is concerned, to through matter gamma rays lose their 
distinguish betw een the longest gamma energv , and hence are absorbed, m 
rays and the shortest X-raj 8 but it is several ways, three being important 
usual to employ the term gamma rays enough to require consideration here 
when the radiations originate within ^he first, vv hich is mo^t significant for 
the nucleus and X-rays when they gamma rays of low energy, and for ab- 
arc formed outside It was seen m sorbers of high atomic weight, is the 
§ 4 71 that characteristic X ravs result photoelectric effect (^2 48), whereby 
from transitions between electronic en- electrons are ejected from atoms or 
ergy levels, gamma rays on the other molecules encountered by the raon 
hand, are associated with transitions ^ is energy of a gamma 

between nuclear energy levels But photon (§3 34), then in a photo- 
once the energv is liberated the prop- electric encounter an amount P , equal 
erties of the resulting radiation arc binding energy of the electron 

determmed by the frequency or wave atom, will be required to remove 

length or in other w ords by the mag- I’h® electron, and the w hole of the re- 
nitude of the energy quantum In this mainder E — P is earned off by the 
respect gamma rays and X-rays are electron in the form of kinetic energy 
Very similar Gamma ray s accompany ^ The second factor contributmg 
many, if not all radioactive changes to the absorption of gamma rays is 
irrespective of whether alpha or beta the Compton effect (§ 3 35), this plays 
particles are emitted But, because major role when the absorber is a 
alpha particles have a discrete enei^ material of low atomic weight, and 
spectrum, the study of alpha dismte- the energy of the radiation is neither 
grations accompanied by gamma rays too high nor too low Nevertheless 
has thrown much light on the nature mcrease of the atomic weight of the 
of the latter radiation absorber increases the extent of ah" 

7 68 Gamma ray s, like X-rays, are sorption caused by the Compton effect 



Nuclear Radiations 169 


'Wlxcti a gatnma-ray photon collides 
with a free or loosely-bound electron, 
the tatter removes some, but not all, 
of tte energy of the radiation. The 
actual loss of energy depends on the 
scattering angle of the gamma rays, 
i.e., on the angle between the direction 
of tic rays before and after collision 
with the electron. In any event, as a 
result of a .scries of Compton encoun- 
ters, in passing through an ajjprcciable 
thickness of absorber, the energy of the 
gamma rays maj" be so gioatl}’’ dimin- 
ished that tho.y .are no longer dctcct- 
al-lc. 

7.70. For gamma rays of high en- 
ergy the photoelectric and Compton 
elTccts are not .so important for their 
.absorption, e.spccially in elements of 
high atomic weight, as is the third 
factor, the foiTn.ation of po.sitron-elec- 
Iron pains (§ 2.71). As shown in Chap- 
ter III, the process requiro.s a minimum 
energy* of 1.02 INIcv, and hence it can 
have no influence on gamma radia- 
tion.s with Ic.ss than this energy. The 
effect increases rapidly, however, as 
the energy of rhe gamma-raj'- photon 
exceeds the minimum v.alue. Tlie prob- 
ability of pair formation increases with 
the square of the atomic number of the 
ahsurhor; this explains why gamma 
rc.vK Irom thorium C", with an energy 
of 2.G2 Mev, roiidily ]>roduoe ])os'itron- 
ciectrou pains when they p.ass through 
ic;ui. Fo). absorbers of high atomic 
■'vcight and gamma rays of high en- 
<'Ty, pair-production is the main cause 
of the cnerg)' loss. 

^ 7.71, As a rc.sult of the interactions 
‘(•ading to the photoelectric effect and 
to p.’iir production, the gamma-r.ay 
photon loses the whole of its cnovgx* 
smd reastes to exist. In a Compton en- 
counter, on the other hand, the photon 

''•'’Privc'd of a p.ari only of its cnergx', 
nu'ntionr-d above: neverthelnss, a 
t'-ur pri>poriion Is transferred to tbc_ re- 


coil electron (§ 3.35). Consequently, 
for each interaction between a gamma- 
ray photon and matter, the result is 
cither the ejection of an electron or the 
formation of a positron-electron pair 
canying a considerable amount of en- 
ergjn It is the ionization (§ 6.5) caused 
b}' these sccondai’}’’ electrons, produced 
in the gas or ejected from the waUs of 
the counter, which provides a means 
for the detection of gamma rays, as 
described in Chapter 6. 

AbSOKPTIOX of GAM^LA. RaYS 

7.72. The absorption of gamma r.ays 
is studied in a manner similar to that 
described for beta pai’ticlcs (§ 7.59), 
e.xcept that the greater i^enetrating 
pov’cr requires the use of a heavy metal 
of high atomic weight, such as lead, 
in place of aluminum, as absorber. For 
homogeneous gamma rays, consisting 
of radiations of a single frequency, or 
wave length, the plot of the logarithm 
of the counting rate (or intensity) 
again.st the thickness of the alisorber 
is strictly linear. In mathematical lan- 
guage, thi.s me.ans that the intensity 
of the radiation falls off exponent! allj'’ 
vith the Thickness of the absorber, so 
that if 7o is the intensity (or counting 
rote) of gamma rays from a given 
source when no absorber is used, and I 
i.s the intensity after passing through 
a thickness of x cm. of absorber, then 

I = Joc-^, (7.16) 

where c is the base of natural loga- 
rithms, and /.i is a characteristic prop- 
erty of the absorber, known as its ab- 
sorption coefficient for the given gamma 
rays. The value of the absorption co- 
efficient varies with the energy of the 
radiation, and it may be used, as e.x- 
piained below, to derive the gamma- 
ray energy. 

7.73. If the radiation consists of sev- 



168 Somcehool, on Atomic Unergy Chap Mi 


come available a considerable number 
of beta-emittmg radioelemcnts whidi 
do not occur m nature from an exam- 
ination of these substances it appears 
that there are several other Sargent 
curves, representing increasingly for- 
bidden transitions below the two 
curves for the natural radioactive ele- 
ments In the opinion of N Feather 
expressed in 1948 there is possibly a 

THE PROPERTIES OF 

Gamma Ray Intehaction 
WITH Matteh 

7 67 As recorded m § 2 104, gamma 
raj s are electromagnetic radiations sim- 
ilar to Xraj« but of shorter wave 
length Actually it is not possible as 
far as their beha\ior is concerned, to 
distinguish between the longest gamma 
rays and the sho’^test X rays, but it is 
usual to employ the term gamma rajs 
when the radiations originate within 
the nucleus and X rays when they 
are formed outside It u os seen m 
§ 4 71 that characteristic X rays result 
from transitions betw een electronic en- 
ergy levels, gamma rays on the other 
hand, are associated wnth transitions 
between nuclear energj le\els But 
once the energy is liberated the prop- 
erties of the resulting radiation arc 
determined by the frequency or wa^e 
length or, m other words by the mag- 
mtude of the energy quantum In this 
respect gamma rays and X rays are 
very similar Gamma raj s accompanj 
raanj, if not all radioactive changes 
irrespective of whether alpha oi beta 
particles are emitted But, because 
alpha particles have a discrete energj 
spectrum, the study of alpha disinte- 
grations accompanied by gamma rijs 
has throwTi much light on the nature 
of the latter radiation 

7 68 Gamma rays, like X-raj^ are 


curve lying in betw een the latter whicii 
actually represents forbidden transi 
tions of the first degree In this case 
the lower Sargent curve of Fig 7 9 cor 
responds to transitions of the secord 
degree of forbiddenness The subject 
13 still m a state of development and 
there is little doubt that its study will 
ultimately contribute to a fuller under 
standing of nuclear structure 

GAMMA RADUTION 

highly penetrating, the effective range 
depends on the energj, but it might 
require several centimeters of metal io 
reduce the intensity of gamma radia- 
tion to such an extent that it becomes 
difficult to detect In their passage 
through matter gamma rays lose their 
energj, and hence are absorbed m 
several ways, three being important 
enough to require consideration here 
The first, which is most significant for 
gamma rays of low energy, and for ab- 
sorbers of high atomic weight is the 
photoelectric effect (§2 48), 'nherebj 
electrons are ejected from atoms or 
molecules encountered bj the radia 
tion If E IS the energy of a gamma 
ray photon (§ 3 34), then in a photo- 
electric encounter an amount P, equal 
to the binding energy of the electron 
m the atom, will be required to remove 
the electron, and the whole of the re- 
mainder B — P IS earned off by the 
electron in the form of kinetic energy 
7 69 The second factor contributing 
to the absorption of gamma rajs is 
the Compton effect (| 3 35), this plays 
a major role when the absorber is a 
matenal of low atomic weight and 
the energy of the radiation is neither 
too high nor too low Nevertheless 
increase of the atomic weight of the 
absorber increases the extent of ab- 
sorption caused by the Compton effect 



NvcUar Radiations 


IHicn a gamma-ray photon collides 
v,'ifh a free or loo.sel.y-bound electron. 
<he latter removes some, but not all, 
of tie energy of the radiation. The 
actual loss of energy depends on the 
fccaltoring angle of the gamma ray.s, 
i.e., on the angle between the direction 
of tie rays before and after collision 
with the electron. In any event, as a 
re-sult of a .series of Compton encoun- 
ters, in p.assing through an appreciable 
thickness of absorber, the energy of the 
gamma raj's may be so gieatly dimin- 
i'jhctl that they are no longer detect- 
able, 

7.70. For gamma rays of high en- 
ergj' the photoelectric and Compton 
effects arc not .so important for their 
absorption, e.speciall}' in elements of 
high atomic weight, as is the third 
factor, the formation of positron-elec- 
tron pfiirs (§ 2.71). As .shown in Chap- 
ter III, the procc.ss requires a minimum 
energy of 1.02 hicv, .and hence it can 
have no influence on gamma radia- 
tions with less than this energy. The 
eiicct incren.sos rapidly, however, as 
t!io energy of the gamma-raj’' photon 
exceeds the minimunt value. The prob- 
ability of pair fonnation increases with 
tile stjuaro of the atomic number of the 
ab^^orber; this c.\'i)lain3 whj' g.ainm.a 
niy.s from thorium C", with an energy 
ot 2.02 IMev, readily produce positron- 
election pairs when they pass through 
lead. For ab.-^orbers of high atomic 
ivfiglu and gamma rays of high en- 

pair-production is the main cause 
of the energy loss. 

7.71. A.s a result of the interaction.s 
leading to the photoelectric effect and 
b> pair production, the gamma-ray 
photon lo.'^es the whole of its cnci'gij' 
and ce.'ises to e.xi.s-t. In a Compton en- 
vnnuer, on the other hand, the photon 
!■' deprived of a part only of its oatergy, 
Vl nienlioncd above; nc'verthelfi.-:s, a 
tasr proportion is transferred to the, re- 


169 

coil electron (§3.35). Consequently, 
for each interaction between a gamma- 
ray photon and matter, the result is 
cither the ejection of an electron or the 
formation of a positron-electron pair 
carrjdng a considerable amount of en- 
ergj^ It is the ionization (§ 6.5) caused 
b}' these .secondao’’ electrons, produced 
in the gas or ejected from the wmlls of 
the counter, which provides a means 
for the detection of gamma rays, as 
described in Chapter 6. 

Absorptiox of G.vxima Rays 

7.72. The absorption of gamma ra3^s 
is .studied in a manner similar to that 
described for beta particles (§ 7.59), 
e.xcept that the greater penetrating 
pow'or requires the use of a heavy metol 
of high ulomic weight, .sucli as lead, 
in place of aluminum, as absorber. For 
homogeneous gamma rays, consisting 
of radiations of a single frequency, or 
wave length, the plot of the logarithm 
of the counting rate (or intensitt^ 
against the thickness of the absorber 
is strictly linear. In mathematical lan- 
guage, this means that the intensity 
of the radiation falls off exponentially 
Avilh the thickness of the absorber, so 
that if lo is the intensity (or counting 
rate) of gamma rays from a given 
source when no absorber is used, and I 
is the intensity after passing through 
a thickness of x cm. of absorber, tiien 

I = (7.16) 

where c is the base of natural loga- 
rithm.s, and fi is a ch.araclcristic prop- 
erty of the absorber, known as its ab- 
sorption coefficient for the given gamma 
rays. Tiie value of the absorption co- 
efficient varies xvith the energy' of the 
radiation, and it may be used, as ex- 
plained below, to derive the gamma- 
ray energy'. 

7.73. If the radiation consists of sov- 



370 


Sourcebook on Atormc Energy Cbay Vll 

eral rays of different energies, the plot log Yt = “"2 

of the loganthm of the intensity against so that 

the absorber thickness mil not be a ^ _ Q ^^3 (718) 

straight line, but rather a combina- 

tion of two or more hues mth different Hence, the absorption coefficient 
slopes In some cases the curves can jjj recjpj-ocal centimeter units, can be 
be analysed so as to give the absorp- readily derived if the half thiclmess, 
tion coefficients for the individual com- centimeters, is known for the given 
ponents of the radiation radiation 

7 74 One of the consequences of 7,75 Another useful quantity is ob- 
the exponential absorption of gamma tamed upon dividing the so-called hn- 
rays is that, theoretically, the intensity absorption coefficient m by the den- 
of the radiation should not fall abso- sity of the absorber, the result, known 
lately to zero no matter how much the mass absorption coefficient, is 
absorber is used The situation is sim- expressed in cm Vgrsm This quan- 
ilar to that considered in § 5 57, m con- ^,ty jg important because it is almost 
nection with radioactive decay How- independent of the nature of the ab- 
ever, even if the absorption equation gorber for low gamma-ray energies, al- 
(7 16) held at very low intensities, though it increases somewhat for ele- 
which is doubtful, the radiation ceases ments of high atomic weight The 
to be detectable so that its intensity is conespondmgnias5Aaf/-^Aicinc88,which 
virtually zero, beyond a certain point nigg not vary greatly with the 
7.76 Several modifications of the absorbing material, is equal to mul- 
absorption coefficient are used m prac- tjpijgd the density, it 13 then ex- 
I ^ce, of which, two may be mentioned pressed m the familiar gram/cm * units 

Oneisthehaf/tticfmess.ie.thethick- „sed m connection with alpha- and 
ness of absorber necessary to reduce beta-particle absorption The absorber 
the ^mma-ray intensity to half its thickness in gram/cm * required to re- 
initial value This quantity lends itself duce the gamma ray intensity by one 
readily to experimental determination, jg j-gjated to the mass absorption 

and it IS simply related to the ab- coefficient by an equation exactly sim- 
sorption coefficient If equation (7 16) ,jar to (7 38) 

is converted into the equivalent form 7 77 jhe fact that the mass half- 
involving ordinary (Briggsian) loga- thickness, 1 e , the actual (or linear) 
nthms [see equation (5 4)], the result thickness multiplied by the den- 
can be written as g,ty^ jg almost independent of the na- 

ture of the material absorbing the 
loG (7/Jn) * -0 4343ur (7 17) gamma rays, means that the higher 

the density the smaller the thickness 
required of a given matenal to decrease 
When the intensity of the gamma rays tiie radiation intensity to a specified 
IS reduced by the absorber to half its extent For this reason, heavy metals, 
initial value, I/7o is and * is the such as iron and, particularly, lead, 
half thickness, represented by x^, are used for shielding from both gamma 
equation (7 17) then becomes rays and X-rays * It is of interest to 

•High atomic weight gives an added advantage especially for radiations of high energy 



Niickar lindialionsi 


note that the approximate constancj" 
of the mass atjsorption coefficient and 
of the mass half-tluckness means that 
the weights of different materials re- 
quirerl to decrease the radiation inten- 
sity by a definite fraction are very 
nearly* the same. But for substances 
of higher density, the volume, and 
hence the thickness, will be less than 
for materials of lower density. 

7.78. Wien using lead as absorber 
for gamma radiation of about 1 Mev 
cnerg.v, the masshalf-thickness is found 
to be about 9.8 gram/cm."; the mass 
absorption coefiicient is then 0.693/9.8, 
i.c., 0.071 cm.Vgram. Approximately 
the same value applies to other ele- 
ments of high atomic weight. The 
(linear) absorption coefficient n is ob- 
tained upon multiplying by the den- 
sity, but the resulting quantity varies 
appreciably from one element to an- 
other. 

Deteumination of Gam.ma-Eay 
Eneugies 

7.79. Several methods luave been em- 
ployed for ascertaining the energies of 
gamma rays. The most direct jjroce- 
durc is to determine the wave length, 
and hence the frequenej', by using a 
cr>-,stal as a diffraction grating (§ 2.88), 
The energj' of the photon is then given 
by the quantum theory relationship 

~ hi', where h is Planck’s constant 
and j' is the frequency of the radiation 
(§ 3.30). The result. can be expressed 
in Mev by means of the conversion 
factors given in § 3.S1. Since the dif- 
fraction measurements become more 
difficuU a,s the cnerg>' of the photon 
increasc,H and the wave length of the 
mdiation decrease.?, the method has 
been used for gamma ray.s of enorgj' up 
to about 0.75 ?vtev only. Gamma-r.ay 
energies from radioelcment-s ocrurring 


171 

in nature range from about 0.04 to 
3.2 Mev^ 

7.80. It was seen in § 7.68 that in 
the photoelectric absorption of gamma 
radiation the kinetic energy of the 
photoclcctron is equal to E — P, where 
E is the energy of the gamma-ray 
photon and P is the binding energy of 
the electron. The kinetic energy of 
the electron can be measured by means 
of a suitable magnetic spectrograph 
(§ 7.44), or by determining its range 
in aluminum (§ 7.62); and the binding 
energy can be calculated from the wave 
lengths of the characteristic X-rays of 
the absorber, usually lead. From these 
two quantities the energy of the gamma 
raj'' can be obtained. The Compton 
recoil electrons (§ 3.35), re.sulting from 
the collisions of the gamma ray pho- 
tons with electrons from a light ele- 
ment, suclr as carbon or aluminum, can 
also be used for determining the energy 
of the photons. The energy of these 
electrons, measured by deflection in a 
magnetic field, or in other ways, is 
related in a fairly simple manner to 
the gamma-ray energj'. 

7.81. Other ways- in which energies 
can be derived will be referred to be- 
low, but one convenient, if not too 
accurate, procedure may be mentioned 
at this point. Theoretical equations 
have been deduced for the extent of 
absorption of gamma rays by certain 
metals, notably aluminum and lead, 
by the photoelectric effect, the Comp- 
ton effect and positron-electron pair 
production, for photons of v.arious en- 
ergies. By adding the contributions of 
the three factors mentioned, curv'cs 
Iiave been drauTi relating the absorp- 
tion coefiicient to the gamma-ray en- 
ergj'. Although the theoretical curves 
are not in exact agreement with ex- 
periment, they can be used to give a 
fair indication of the energy from a 



172 


Sourcebook on Atomic Energy Chap VII 


knowledge of the absorption coefficient 
for the given gamma radiation * 

Origin of Gaaima Rays 
7 82 Perhaps the most striking e\i 
dence that gamma rajs are due to 
transitions betiveen energj le\els is 
provided bj the correlation between 
alpha particle and gamma ray ener 
gies The thorium C— *thmmm G" 
ciismtegratian refcired to m ^ 7 SDsup 
phes convenient d ita tor ilJusliating 
the arguments Before proceeding to 
the calculations hone\cr it must be 
Iiomtcd out that the measured alpha 
particle energy docs not give the total 
energy accompain mg a t’^onsni in bo- 
cause p xrt of the energy is u ed up m 
the recoil of the dauijhter nucleus 
The relatiN e masses of the thorium C ' 
nucleus and of the alpiia paiticle aic 
20S and 4 respertivelj on the atomic 
Meiglit scale hence it can b« readilj 
shown assuming conseraation of mo- 
mentum thatthototalenergj liberated 
m i given transition is (208 4)/208 

times the energy cained off by the 
alpha particle The values obtained 
m this way together v\ith the corre- 
sponding alpha particle energies are 
given in the accompanj mg table The 
third column contim-s the differences 
betueen the disintegration energy for 
a given group of alpha particles and 
the V ilue for the first group Since the 


THoniuM C 

— * Tnomuii C 

TiuxsmoNS 

Alpha 

Particle 

Dinnleprolion 

Difference 

from 

hnergj 

Energy 

First Group 

(Mev) 

(Mev) 

(Mev) 

S0S4 

6 201 

— 

G044 

6 161 

0040 

5 762 

5 873 

0 328 

5 6'’0 

5 728 

0 473 

5 601 

5 709 

0 492 


latter is the highest it may be sup 
posed to represent the transition from 
tlionum C to the lov\ est nuclear energy 
level of thorium C" the energy differ- 
ences m the last column are tlicn the 
energies of the higher (excited) levels 
of thorium C as compared with the 
lowest level 

7 83 Wlien m a radioactive change 
the daughter nucleus is formed m an 
excited state it is believed that within 
a very short interv al of time, some- 
where about sec , it releases its 
exce&s energy m the form of a gamma 



Tie 7 10 Tran itnns between nuclear 
energy levels m tlioi iiira C correlated with 
gamma ray energies 


ray photon and passes into a lower 
energj state If this is true then there 
should lie a connection between the 
energies of the gamma laj** accom 
panying the thorium C — » thorium C ' 
piocess and the energies of the various 
lev els deriv ed above Such is undoubt- 
edly the ca«e Siv gamma rajs with 
enei^ies of 0 040, 0 327, 0 287, 0 471, 
0 432 and 0 451 hlev, respectively, 
liave been detected m this radioactive 
change and it can be seen from Fig 
7 10 that these values can be accounted 
for, nithm about 0 001 Mev, by the 
transitions indicated by arrows 

7 84 The intensities of the gamma 


• Because the absorption coefficient passes tlmn^h a mmimum w ith increasing gamma-ray 
energy there are usually two energy values corresponding to a given absorption coefficient 
By making measurements with two different absorbers the correct energy value may be 
chosen 



Nuclear Tiadlalions 


rays indicate that the transitions 2 — » 1 
mid 5 — > 2 arc the most probable. The 
o~*l transition is evidently highly 
forbidden by the appropriate selection 
rules (§7.G5). The transition from 
level 5 to level 1 must take place in 
two stages, namel)', 5-^2 followed 
by 2 — 1 ; on the other hand, the 
(vansition 4-^1 can take place di- 
rectly, or in the two steps 4-^2 and 
2 —V 1. The transition 5 — i 3 is ap- 
parently also forbidden, for the cor- 
responding gamma raj' would have an 
energy of 0.1G4 IMev, which would 
have been delected had it been present. 

7.85. Several instances of radioac- 
tive changes accompanied by gamma 
rays, some in association with the emis- 
sion of alpha particles and others with 
beta particles, have been investigated 
in a manner .similar to that described 
for the thorium C — i thorium C" dis- 
integration. In every case the energies 
of the gamma rays can be explained 
quantitatively in terms of transitions 
between nuclear levels whose energies 
have been derived from those of the 
alpha .and beta particles, as described 
nboi'c. Thus, gamma rays may be 
rep.arded as a form of nuclear spectrum 
which provides information concerning 
nuclear energj^ levels, just as optical 
and X-ray .spectra pcmiit the inter- 
pretation of electronic levels. It is of 
interest to mention in this connection 
that the analogy can be extended, in 
some measure, to nonradioactive cle- 
nients. By .^uiiplying sufRciont energy, 
the nuclei of a number of stable cle- 
nicnl.s can be rai,scd to e.xcited energy' 
.'•'tates which then decay, at a measur- 
able mte, lo the normal state while 
f'nwtmg gamma radiation (§ 10.127). 

lNTr.ux.\ji, Coxvnnsiox 

OF Ikvvs 

1,86. Isfful information concerning 
gamma rays has been ubtaiued from 


173 

the phenomenon now known as internal 
conversion. In 1914, E. Rutherford 
suggested the possibility that in emerg- 
ing from a nucleus the gamma ray 
(photon) may produce a kind of photo- 
electric effect with one of the orbital 
electrons of the same atom, in which 
the whole of the energy is transferred 
to the electron. The gamma ray is 
then said to be internally converted. 
The electron which interacts wdth the 
gamma-ray photon is ejected from the 
atom w'ilh kinetic energy equal to 
E — P, where, as before, E is the 
gamma-ray'- energy quantum and P is 
the binding energy’’ of the electron in 
the atom of the radioelement emit- 
ting the gamma radiation. This is pre- 
sumed to be the daughter element in 
the given disintegration. If the ejected 
electron came from the first quantum 
level of the atom, usually called the 
K level (§ 4.72), then P can be re- 
placed by Ek, w'hei’e Ek, according 
to the theory of the origin of X-ray's, 
is the energy of the K line of the char- 
acteristic X-rays of the daughter ele- 
ment. Hence, the electron should be 
ejected vvith a kinetic energy’- of P — Ek- 
Similarly, if the electron originates in 
the second (L) level, its kinetic energy' 
should be E — El. 

7.87. If the gamma-ray' energy E 
has a definite value, then as a result 
of internal conversion there should be 
emitted a number of groups of elec- 
trons hav-ing discrete energies. There 
is no doubt that these are the second- 
ary' electrons, having definite energy' 
values, that have long been known to 
accompany the primary beta p.aiiicles 
which exhibit a continuous distribution 
of energy' (§7.43). Because of their 
definite energies, the internal conver- 
sion electrons are .said to give a line 
f-pcctnim. as distinct from the oontinu- 
ou.'^ .spectrum of the beta particles. It 
siionld be mentioned here that, as a 



174 


) 


Sourc^ook on Aiomtc Energy Chay YU 


general rule, only a small proportion 
of the gamma-ray photons have their 
energy intenially converted, the frac- 
tion so converted, called the internal 
conversion coe^cienf, usually decreases 
with mcreasmg energy of the gamma 
rays 

7 88 The vahdity of the preceding 
arguments can be checked m several 
ways The energies of the internal 
conversion electrons has been deter- 
mined in a number of instances, by 
the magnetic spectrograph, and adding 
to these the energy values for the ap- 
propriate K, L, etc , lines of the char- 
acteristic X-ray spectrum of the daugh- 
ter element should give the energies 
of the gamma rays prior to conversion 
A case which has been thoroughly stud- 
ied IS the electron Ime-spectrum of the 
process radium B — * radium C A few 
of the measured kmetic energies are 
given in the table together wth the 
binding energies derived from X-ray 
data of radium C, these are added 
and compared ivith the accepted values 
for the energies of five gamma rays 
The excellent agreement of the figures 


Ex-ECTBON Li>E SPEcTTRUlt AND GaMMA 
Rays for the Radium B — • Radium C 
Transition 


of 

Electron 

(Mev) 

1 c 

X-Rcj 

1 Ltne 

1 

1 Bindinu 
■ Energy 
(Mev) 

1 

1 Total 

1 Energy 
(Mev) 

! Bay 
\ Energy 
(Mev) 

0 036S 

£ 

00161 

00529 

00529 

OISIO 

■ A 

0 0S87 

0 2397 

0240 

0 1617 

, K 

0 0887 

02564 

0257 

0 2041 

K 

0 0887 

0 2920 

0293 

0 2605 

h 

0 0887 

0 3493 

0 350 


m the last two columns pro\ ides sup- 
port for the vievs presented above 
Incidentally, the determination of the 
energies of the conversion electrons 


thus represents another method for 
evaluating gamma-ray energies 
7 89 It will be noted that the 0 0529 
Mev gamma ray ejects an L electron 
but not a K electron, the reason is that 
the removal of the K electron requires 
0 0887 Mev, which is greater than the 
energy available m this case The other 
rays expel L, M and N electrons, m 
addition to the K electrons, but the 
results are not recorded here 
7.90 When a gamma ray is inter- 
nally converted and ejects a K, L, etc , 
electron, it is to be anticipated that 
the vacancy will be filled by one of the 
other electrons m the atom From 
what has been stated m 1 4 72, it is 
apparent that this process should he 
accompanied by the emission of the 
K, L, etc , line of the charactenstio 
X-mys of the daughter element Such 
X-rays have, m fact, been observed in 
several instances of internal conver- 
sion, and the energies are found to 
be just as expected according to theory 
7 91. A final point is worthy of men- 
tion m conclusion It has been tacitly 
accepted, so far, that gamma rays are 
due to transitions betw een energy lev- 
els in the daughter nucleus, rather than 
m that of the parent, for a given radio- 
active decay That this assumption is 
justified IS shown by the observations 
made in connection with internal con- 
version phenomena The binding en- 
ergies of the electrons, obtained by 
subtracting their measured kinetic en- 
ergies from the known gamma-ray 
energies, and the observed frequencies 
of the characteristic X-rays, to which 
reference has just been made, are defi- 
nitely those of the daughter, and not 
of the parent, clement These facts 
provide clear proof of the contention 
that the gamma rays are emitted from 
the excited daughter nucleus which 
remains after the parent has ejected 
either an alpha or a beta particle 



Isotopes 


Chapter VIII 


THE DISCO^TSHY OF ISOTOPES 


Radioelements and the 
Peihodic System 

8.1. By 1911, nearly forty specie.s 
with different radioactive properties 
were known, bnt only twelve positions 
were available to accommodate them 
in the periodic table (§ 1.44). The 
obvious question then was: How can 
forty elements be fitted into tivelve 
places? It was apparent 'that if the 
periodic classification was not to break 
down'completel)'' in the high atomic 
\veight region, .several radioactive spe- 
cies would have to occupy one position, 
at -least in certain cases. Some evi- 
dence for this possibility had been 
obtained by a number of investigators, 
including H. N. McCoy and B. B. 
Boltwood in the United States (sec 
§0.4-1), W. Marclevvald in Germany, 
and F. Soddy in Great Britain. It had 
been found that certain groups of 
'‘elements,” h.a^^ng quite distinct ra- 
dio.aetivc properties, could not be sepa- 
rated by any chemical means avail- 
able.* In spite of the difference in the 
nature of the disintegrations, the spe- 
cies within each of the groups appeared 


to be identical chemically. Reviewing 
the situation at the end of 1910, Soddy 
said: “The evidence of chemical iden- 
tity is not of equal weight for all the 
. . . cases, but the complete identity 
of ionium, thorium and radiothorium, 
of radium and mesothorium-l, and of 
lead and radium D may be considered 
thoroughly \vell established.” In the 
same review, attention was called to 
the identity of the three gaseous ema- 
nations ivhich have properties analo- 
gous to those of the inert gases of the 
atmosphere. 

8.2. The chemistry’- of radium, being 
very similar to that of barium, pre- 
sumably placed it in the alkaline-earth 
family, that is, in Group II of the 
pei'iodic table (§ 1.46), w'hereas the 
properties of thorium appeared to 
make it fit best into Group W.f The 
emanations undoubtedly belong to 
Group 0, and so it is possible to draw 
up the accompanying scheme for two 
of the alpharemitting stages of the 
uranium and thorium series (§ 5.58), 
based on the identity of chemical 
properties mentioned above. 


GROUP IV II 0 

Thorium IMo.solhorium Emanation 

Ionium lU Radium ^ Emanation 

; ‘^icCoy and tV. H. Ross, at the University of Cfiicago, were apparently the first, 

difTercnl radiocleincnls might he identical chcmicnlb’. In spite of 
P>'i'ripit.atioiis, using oxalic acid, chromate, thiosulfate, hydrogen pero>ndc or 
tjjey were unable to cause any detectable separation of radiothorium from thorium. 
JW‘-.-ib!o.ihat thorium may l>e a member of the actinide .scries of elements (§§ 1.49 
not actually in Group IV; ho-ivcver, its most stable compounds 
0 . four, xvhich is cbaractcri-stic of Group IV, and Ibi.s Is really the point of the 



174 


Sourcehook on Atomic Energy Chap Vll 


general rule, only a small proportion 
of the gamma-ray photons have their 
energy internally converted, the frac- 
tion so converted, called the infernal 
conversion coefficient, usually decreases 
with increasing energy of the gamma 
rays 

7 88 The validity of the preceding 
arguments can be checked m seiteral 
ways The energies of the internal 
conversion electrons has been deter- 
mined in a number of instances, by 
the magnetic spectrograph and adding 
to these the energy values for the ap- 
propnate K L, etc , lines of the char- 
acteristic X ray spectrum of the daugh- 
ter element should give the energies 
of the gamma rays prior to conversion 
A case which has been thoroughly stud- 
ied IS the electron Ime-spectrum of the 
process radium B — * radium C A few 
of the measured kinetic energies are 
given m the table together with the 
binding energies derived from X-ray 
data of radium C, these are added 
and compared with the accepted values 
for the energies of five gamma rays 
The excellent agreement of the figures 


EliECtRON I INE SPECmuM AND GaMMA 
Rays for the Radium B — ♦ RADimu C 
Transition 


Energj Radium 
of C 

Eltdron X Raj 
(Mev) Line 

Binding 
' Energy 
(Mev) 

Total 

Energy 

(Mev) 

Cemma 

Ray 

Energy 

(Mev) 

0 0368 L 

OOIGI 

0 0529 

00529 

0 1510 A 

' 00SS7 

' 02397 

0240 

0 1617 K 

0 0887 

0 2564 

: 0257 

02041 A 

0 0887 

0 2929 

0293 

0 2605 A 

0 0887 

0 3493 

0 350 


in the last tivo columns proi ides sup- 
port for the vievs presented above 
Incidentally, the determination of the 
energies of the conversion electrons 


thus represents another method for 
evaluating gamma ray energies 

7 89 It ivill be noted that the 0 0529 
Mev gamma ray ejects an L electron 
but not a K electron, the reason is that 
the removal of the K electron requires 
0 0887 Mev, which is greater than the 
energy available in this case The other 
rays expel L, M and A electrons, m 
addition to the K electrons, but the 
results are not recorded here 
7 90 When a gamma ray is inter- 
nally con\ erted and ejects a K, L, etc , 
electron, it is to be anticipated that 
the vacancy will be filled by one of the 
other electrons m the atom From 
what has been stated m § 4 72, it is 
apparent that this process should be 
accompanied by the emission of the 
K, L, etc , line of the characteristic 
X-rays of the daughter element Such 
X-rays have, m fact, been observed m 
several instantcs of internal conver- 
sion, and the energies are found to 
be just as expected according to theory 
7 91 A final point is worthy of men- 
tion in conclusion It has been tacitly 
accepted, so far, that gamma rays are 
due to transitions bet^i een energy lev- 
els m the daughter nucleus, rather than 
in that of the parent, for a given radio- 
active decay That this assumption is 
justified is shown by the observations 
made m connection \vith internal con 
version phenomena The binding en- 
ergies of the electrons, obtained bj 
Bubtractmg their measured kinetic en- 
er^es from the known gamma ray 
energies, and the observed frequencies 
of the characteristic X-rays, to which 
reference has just been made, are defi- 
nitely those of the daughter, and not 
of the parent, element These facts 
provide cleai proof of the contention 
that the gamma rays are emitted from 
the excited daughter nucleus which 
remains after the parent has ejected 
either an alpha or a beta particle 











182 


Sourc^ook on Atomic Energy 


ary m character, since elements had 
previously been regarded os having 
definite atomic weights But it seemed 
inevitable if the group displacement 
law and the concept of isotopes had 
any real basis of fact Experimental 
proof that lead onginating from ura« 
mum has a different atomic weight 
from that derived from thonum, while 
both differ from that of lead obtained 
from nonradioactive sources, would 
thus provide convincing evidence for 
the theory of radioactive decay and the 
existence of isotopes 
8 21 The mineral thorite, from 
Ceylon, consists mainly of thorium 
with relatively little (1 to 2 per cent) 
uramum, and about 0 4 per cent of 
lead, hence, it seemed likely that the 
latter was produced entirely by radio- 
active decay of the thorium Conse- 
quently, Soddy, m conjunction with 
H Hyman, set out to extract and 
punfy the lead from thorite, and then 
to determine its atomic weight They 
obtained i 2 grams of purified lead 
\ chloride, and determined the atomic 
weight by making comparison meas- 
urements wth lead chloride from a 
nonradioactive source In May 1914 
it was reported that, in agreement with 
expectation, the atomic weight of the 
thonum lead was about one unit higher , 
than that of ordinary lead 
B22 Become of tho dj3eu}ijes as- 
sociated with the accurate determi- 
nation of atomic weights, especially 
when working with small amounts of 
material, M E Lembert came from 
Germany, at the suggestion of K 
Fajans, to study the atomic weights of 
lead from vanous sources in the Har- 
vard Umversity laboratory of T W 
Richards, who was recogn*xed as the 
leading authority in this field of in- 
vestigation In 1914, Richards and 
Lembert made direct determinations 
of the atomic weight of lead extracted 


Chap VIII 
from several uranium minerals and in 
every case they found the values to be 
definitely lower than that of ordinary 
lead The lowest result obtained was 
206 40 for lead from uranmite, found 
m North Carolina, even though the 
figure was not down to 206, the theo- 
retical value, probably because the 
lead was of mixed ongm, the low value 
was nevertheless significant The same 
conclusion, that the atomic weight of 
lead from uranium minerals was less 
than that of ordinary lead, was also 
reached independently by Maunce 
Curie m France, and by 0 H6nig- 
schmid and S Horovitz m Austria 
during the jear 1914, so that the 
accuracy of the result could not be in 
serious doubt 

8 23 In reporting, in the early part 
of 1915, on the work dealing with the 
atomic weight of lead from radioactive 
sources, Soddy WTOte “Bearing in 
mmd that two of the four researches 
have been earned out by chemists 
[Richards and Honigschmid] expen- 
cnced in atomic w eight determinations, 
and that much of the mineral examined 
was no doubt of very mixed compo- 
sition, so that not all the lead present 
j can be reasonably assumed to have 
been of radioactive ongm, it is clear 
that the theoretical predictions have 
received remarkable confirmation 
that 022 222 reot 2 gato 2 ' sso experienced jn 
atomic-weight work as Professor T W 
Richards should regard his results as 
definitely establishing a variation in 
the chemical equivalent of lead from 
different sources is perhaps the 
chief result gamed ” Soddy indicated 
that the data available at that time 
were still of a somewhat preliminary 
nature, and he said that “further re- 
sults with carefully selected minerals 
must be awaited “ 

8 24 Actually, subsequent measure- 
ments, made with the greatest care, 


iROtopCS 


have amply confirmed the earlier re- 
sults. Some of the more interesting 
values are tabulated here; they maj' he 


183 

erals have atomic weights differing by 
nearly two units, they are completely 
identical and indistinguishable in their 


Atomic Weight ok Leah from Radioac'tive Minehaes 


THIAHHIM MIEEIIAI-.S SoUTCC A(oW7C Ji Clff/lf l7lVCSilQ^(OT 

Clcvcilc, Norway 206.0S T. W. Richards 

Brfiggcritc Norway 206.01 T. W. Richards 

Pitchblende W. Africa 206.05 0. Honigsehmid 

Koim Sweden 20G.01 G. P. Baxter 

TnOIUU.M MINEHAI.S 

Thorite Cejdon 207,8 0. Honigsehmid 

Thorite Norway 207.9 0. Honigsehmid 


compared with the atomic weight of 
207.2 for lead from nonradioactive 
sources. The striking agreement with 
theoretical e.vpectation, which pre- 
dicted the atomic weights of lead from 
uranium and thorium to be 206 and 
20S, rcs]3cctivcly, provides the strong- 
est possible, support not only for the 
grovip displacement law, but also for 
the whole theory of radioactive dis- 
integration. It required (he latter to 
predict the atomic weights of the end 
products, and it w.as a combination of 
both whicli indicated that they should 
bo chemically indistinguishable from 
load. 

8.25. The results just described have 
an important significance apart from 
their bearing on the theories of radio- 
actir-ity and the ])roblcm of the ac- 
commodation of the knowm radioele- 
inents in the limited number of places 
av.ailablc in the periodic system. The 
existence of radioactive isotopes with 
different atomic weights, occup 3 dng 
the same, po.rition in the periodic tabic 
and having identical chemical proper- 
ties, may perhaps not be considered 
.surprising, ])ut the remarkable fact is 
that an ordinarj', nonrndioactive ele- 
ment like lend can also exist in isotopic 
fonns. Thus, although the various 
j'Pecimen.s of nonradioactive lead sepa- 
nued from uranium and thorium min- 


chomical properties. The discovery of 
the existence of stable isotopes of lead 
indicated the possibilitj’- that other 
nonradioactive elements might occur 
in isotopic forms, and in this connec- 
tion concurrent developments in an 
apparentl.v unrelated field were des- 
tined to play an important part. 

Positive-Ray Analysis 

8.26. As stated in § 2.62, the raj'^s of 
positively charged particles formed bj’’ 
tlie passage of an electrical discharge 
through an evacuated tube had been 



Fig. 8,2. Principle of positive-raj’ 
analysis, 

shonm by W. Wien to consist of atomic 
or molecular ions of the gas present in 
the tube. The nature of these ions can 
be investigated by studjdng the deflec- 
tion of the positive raj’s in electric and 


184 


Sourcebook on AUmtc Energy 


magnetic fields, making use of a pnn- 
ciple first employed by W Kaufmann 
in 1901 for beta particles (electrons), 
and m the following year by Wien for 
positive rays 

8 27. A narrow beam of positively 
charged particles, such as constitute 
the positive rays, will normally travel 
m a straight line, but if subjected to an 
electnc or magnetic field the beam will 
be deviated from its original direction 
Imagine a single positively charged 
particle moving downward perpendicu- 
lar to the plane of the paper, striking it 
at the pomt 0 in Fig 8 2 Suppose a 
uniform electric field of strength E is 
applied so that the particle is deflected 
to the nght and stnkes the paper at X, 
the distance x from 0 to X is then 
given by 



where ki js a constant depending on the 
dimensions of the apparatus, e is the 
charge on the particle, which must be a 
multiple of the electronic charge, and 
m and v are the mass and velocity, 
respectively, of the positive particle 
8 28 Suppose, however, that in- 
stead of the electnc field, a magnetic 
field H IS used to deflect the particle m 
a direction perpendicular to OX, so 
that it strikes the plane of the paper at 
Y, the displacement y from 0 to F is 
now expressed by 

(82) 

mv 

where fcj is also dependent on the 
dimensions of the apparatus By ap- 
plying the electnc and magnetic fields 
Bimultaneouslv, the particle is de- 
flected to P, the coordinates of which 


Chap nil 
are determined by x and y, as given by 
equations (8 1) and (8 2) If r is 
eliminated from them, it follows that 

fy^. m 

where k is another constant related to 
kt and ki 

8 29. If, instead of one positive par- 
ticle, a beam of positive rays is con- 
sidered, m which all the particles have 
the same ratio of mass m to charge e, 
so that m/e is constant, but not neces 
sarily the same velocity, it follows from 
equation (8 3) that 

X =» constant X j/*, (8 4) 

provided the strengths of the electnc 
and magnetic fields, that is, E and 
H, remain constant The positively- 
charged particles, of constant m/e, 
which are deflected by these fields will 
thus fall on a senes of points, of which 
P IS one, whose coordinates satisfy 
equation (8 4) This expression is the 
mathematical representation of a pa- 
rabola, and so it follo%vs that the 
points when jomed together will form 
a parabolic curve, such as AA m Fig 
82* 

8 30 An examination of equations 
(8 1) and (8 2) shows that, for a given 
particle, the displacements x and y 
depend on the velocity of the particle, 
the ^ater the velocity the smaller the 
displacement, and vice versa The 
senes of points making up the para- 
bolic curve consequently represent pos- 
itive particles wth different velocities, 
but having the same value of the moss- 
to-charge ratio, m/e The fast mov- 
j mg particles are deflected only to a 
1 small extent, while the slower particles 


Tt should be noted that the curve is not a complete parabola but only a portion of one 
it would nevertheless bo described mathematicsdly as a parabola, although the expression 
parabohe curve ’ will be used here 



Isotopes 


fvrc dcncct<?d considerablj’ more. The 
conlimut-y of tlic curve -4/1 would 
imply lhai particles having all possible 
velocities, between certain limits, are 
present in the positive rays. 

8.31. A beam of particles for which 
7 n/c has a value that is constant, 
but different from the one considered 
above, will be deflected by electric and 
magnetic fickls so that the particles 
fall on another parabolic curve BB. 
From equation (8.3) it can be seen that 
the smaller the quantity m/e, the 
larger will be the displacement y for a 
given value of x. The point Q, for 
example, corresponds to a particle 
whose mass-to-charge ratio, m/e, i.s 
smaller than that for the particle fall- 
ing on the point P. In Fig. 8,2, there- 
fore, the parabolic curve BB would be 
formed by the deflection of a stream of 
jiarticlcs of varj’ing velocity, but hav- 
ing a constant value of rn/c which i.9 
smaller than that for the curve AA. 
If the ordinates of the points P and Q, 
for a con.stant value of the displace- 
ment X, arc ijA and i/n, respectively, it 
follows from equation (8.3) that 



whore the quantities (m/e)A and {m/c)ii 
refer to the two .sets of particles falling 
0 !j the curves A A and BB, respec- 
tively. If the charges carried b}' the 
particles .are assumed to bo equal, it is 
Sf-en from equation (8.5) that 



h t'hnuM thus be possible to compare 
the and rnn of particles 

pn-sent m positive ray.s by observing 
their defli'f'tiojis, and yiu for con- 
et iut r. w hen .-subjected to the simui- 


185 

taneous action of electric and magnetic 
fields. 

I 8.32. If a beam of positive rays con- 
tains particles of different masses then 
they will be sorted out in such a man- 
ner that all particles with the same 
mass or, more correctly, all having the 
same v\/e value, will fall on one para- 
bolic cui-ve. A method of posiiive-ray 
analysis, is thus available for detecting 
the presence of, and even for identify- 
ing, atomic and molecular particles 
whose masses differ from each other. 

Positive Rays .and Isotopes 

8.33. In the course of his extended 
studies of positive rays, J. J. Thomson 
(.see § 2.21) made, in 1912, an interest- 
ing observation which has a bearing 
on the existence of isotopes of stable 
elements. An electric discharge was 
passed through a vessel containing the 
experimental gas at suitable low pres- 
sure. A narrow stream of positive rays 
was obtained in a manner similar to 
that described in § 2.61, using a pierced 
aluminum cathode connected to a fine- 
bore brass tube. After passing through 
electric and magnetic fields arranged 
so as to give deflections at right angles 
to one another, as in Fig. 8.2, the 
positive rays were allowed to fall on 
a photographic jilate. Upon develojs- 
ment, the latter showed a series of 
parabolic streaks, each corresponding 
to a definite value of the mass-to- 
charge ratio {m/e) of atomic and 
molecular particles present in the posi- 
tive rays, in accordance with the dis- 
cussion in the preceding section. 

8.34. An illustration of the type of 
result observed is shown in Fig. 8.3. 
Tiiere are here three .sets of posilivc- 
ray parabolas; one corresponds to Fig. 

I S.2, while the others are obtained by 
j reversing, in turn, the direction of 
i cither the magnetic or the electric 
I field. These three groups of curves are 



186 

essentially reflections of one another in 
the X and y axes; hence, the portions 
of these axes can be found and the 
ordinates of points on the curves deter- 
mined. Utilizing the curve produced 
by a substance of known mass, such as 
oxygen, as standard, the masses of 
other atoms and molecules can then be 
calculated by means of equation (8 6^ 
8.35. The positive-ray photograph 


Chap VIII 

Thomson said: . . in addition [to 
the strong neon line] there is a line 
corresponding to an atomic weight of 
22, wWch cannot be identified with the 
bne due to any knoivn gas. I thought 
at first that this line, since its atomic 
weight is one half that of CO 2 , must 
be due to carbonic acid [molecular 
wei^t 44] with a double charge of 
electricity, [so that m/e would be 22], 


Sourcebook on Atomic Energy 


yNe{20) 

//Ne(22) 



Fio 8 3 Thomson's posiU% e-ray parabolas 


obtained by Ihomson exhibited a 
number of interesting features, but the 
aspects to be considered here will be 
restricted to those having a bearing on 
the subject of isotopes It was noted 
that when the discharge tube con- 
tained neon gas, atomic weight 20.2, 
the photographs always showed, in 
addition to the expected neon line, the 
presence of a line indicating a particle 
of mass 22, on the atomic weight scale 
In speaking of this matter in 1913, 


and on some of the plates a faint line at 
44 could be detect^. On passing the 
gas slowly throu^ tubes immersed in 
bquid air [which would remove the 
COj] the Ime at 44 completely dis- 
appeared, while the brightness of the 
one at 22 was not affected. The oripn 
of this line presents many points of 
interest; ‘there are no known gaseous 
compounds of any of the recognized 
elements which have this molecular 
weight. . . The fact that this line is 



Isotopes 

bricht in the sample when the neon fusion and rediffusion, he had ob- 
linc is extraordinarily bright, and in- tained, from 100 cc. of ordina^ neon 
visible . . . when the neon [line] is gas, hvo extreme fractions of 2 to 3 cc., 
comparatively feeble, sugge-sts that it with atomic weights, calculated from 
may possibly be a compound of neon their densities, of 20.15 and 20.28, 
and hydrogen, NeHj, though no direct respectively. ^ 

evidence of the combination of these 8.38. The difference m these atomic 
inert gases has hitherto been found.” wei^ts is small, nevertheless it is 

8.36. Although J. J. Thomson was significant. The fact that the former 

not at all sure of the identity of the gas value is less, while the latter is greater, 
giving the mass 22 line in the positive- than the atomic weight of ordinary 
ray photographs, he felt that there neon showed that a partial separation 
could “be little doubt that what has of the two constituents of neon had 
been called neon is not a single gas, but been acliieved. In his book on Rays of 
a mixture of two gases, one of which Posiiive Electricity, published in 1913, 
has an atomic weiglit of about 20 and Thomson wTote referring to Aston’s 
the other about 22. The parabola due results: ‘‘He obtained sufficient alter- 
to the heavier gas forms only a small ation in the proportion betw'een the two 
percentage of the mixture.” In order gases to produce appreciable changes 
to throw .some light on the situation, in the relative brightness of the two 
the English scientist F. W. Aston, ivho lines [for the masses 20 and 22] in the 
wjus then Thomson's assistant, set out positive-ray photograph, n,nd changes 
to separate the constituents of neon in the density large enough to be 
gas, Tlie first attempt, based on the detected, . . . No differences, how- 
fractional distillation of neon adsorbed ever, could be observed in the spec- 
on charco.al cooled in liquid air, failed trum of the mixture, and this . . . 
to give any detectable separation, and gives some grounds for the suspicion 
so the pos-sibility of separation by that the two gases, although of differ- 
diffusion was tried, ent atomic weights, may be indistin- 

8.37. It has long been known that a guishable in their chemical and spec- 
light gas will diffujie through a porous troscopic properties.” 

partition more rapidly than will a hcav- 8.39. In other words, it seemed 
icr ga.s; consequently, Aston passed possible that neon might exist in two 
neon gas through a pipc-cIay tube, isotopic forms wdth masses of 20 and 
collected that portion of the gas which 22, respectively; this interpretation of 
diffuscil through, and allowed this to the results ivas later confirmed. It 
diffuse once more, and so on. This ma}' be mentioned, however, that for 
procedure proved to be more success- several years Thomson was liimself 
ful. and at the historic meeting of the reluctant to accept this \dew, for he 
British .Association in 1913, to which felt that the possible presence of a 
reference was made in § 8.4, Aston hydrogen compound, such as NeHs, 
aimounced that after repeated dif- could not be ignored. 

THE OCCIJKENCE OF ISOTOPES 

IhiK B not.K Numbku Hulk Europe interfered with the continu- 

8.40, In the jK’riwl from 1914 to fition of Aston’s work on neon, but 
1918 the cxipmcies of the w.ar in upon its resumption his initial efforts 



188 

^\e^e devoted to an attempt at im- 
provmg the degree of separation of the 
two forms of the element by diffusion 
The results were not too promising, 
and Aston came to the conclusion that 
the best approach to the problem 
would be, as he himself stated, to make 
positive-ray studies “with such ac- 
curacy that it could be demonstrated 
with certainty that neither of the two 
atomic weights so determined agree 
with the accepted figure ” Con- 
sequently, with the object of improv- 
ing the accuracy of the measurements 
Aston redesigned the positive-ray de- 
flection apparatus In the instrument 
constructed in 1919, the electric and 
magnetic fields were so arranged that 
all particles having the same mass m ere 
brought to a focus so os to produce a 
fine hne rather than a parabola Since 
each line mdicated the presence of 
atoms or molecules of a particular 
mass, the result was referred to os a 
mas8 spectrum and the instrument was 
called a moss spectrograph 
B 41 With his first mass spectro- 
graph Aston was able to confirm the 
supposition that two forms of neon 
exist with atomic masses almost ex- 
actly 20 and 22, respectively, the 
proportion of the former appeared to 
be approximately ten times the latter, 
so that the mean atomic weight should 
be 20 2^ m excellent ajrreement with 
the accepted value Turning next to 
the faimhar element chlorine, whose 
atomic weight was known with con- 
siderable accuracy to be 35 457, Aston 
found that this also gave a mass spec- 
trum with two Imes corresponding to 
masses very close to 35 and 37, re- 
spectively, there being no indication of 
the presence of a particle ivith a 


Chap Vm 
fractional atomic weight It appeared 
therefore, that dhlonne, bke neon, con- 
sisted of a mixture of at least two 
isotopes 

8 42 By the end of 1920, Aston had 
examined nineteen elements m his 
mass spectrograph and found that 
nine of them consisted of two or more 
isotopic forms with masses which were 
close to integers Further, it was ob- 
served that elements hke helium, car 
bon, nitrogen, oxygen, fluorme and 
phosphorus, which have atomic weights 
close to whole numbers, are not com- 
posite, as are neon, chlorme, boron, 
aigon and other elements * 

8 43 These results led Aston to 
formulate the whole number rule, which 
13 essentially a modified form of R-out's 
hypothesis (§ 1 38) According to this 
rule all atomic weights are very close 
to integers, and the fractional atomic 
weights determined chemically are due 
to the presence of two or more isotopes 
each of which has an approximately 
integral atomic weight t The con- 
stancy of the atomic weights of the 
elements as they occur in nature— 
with the exception of lead from radio- 
active sources — indicates essentially 
constant isotopic composition, that is 
to say, the constituent isotopes of a 
given element are always present m 
substantially the same proportions 

8 44 The possibihty that the chem- 
ical elements might consist of groups 
with virtually identical chemical prop- 
erties, but different atomic weights, 
wi« considered during the ISSOs by 
P Schutzenberger in France and by 
W Crookes in England, both of whom 
thought it possible that the accepted 
atomic weights were mean values for 
the two or more members of the group 


• Later work lias diown that small amounts of isotopes are present m helium carhon 
nitrMcn and oxygen 

t The same general idea had been expressed in 1915 by W D Harkins and E D Wilson 
m the United States and shortly thereafter by K Fajans in Germany and by F Soddy m 
England, but at the time it lacked expeiimenw support 


Sourcebook on AtoTme Energy 



Isotopes 


Crookes was influenced by the chemi- 
cal similarity of the rare-earth ele- 
ments which, at the time, could not 
1 k! fitted inln the periodic table. As 
this difficulty has since been overcome, 
the arguments for “meta-elements,” os 
lie called them, now lack force. It is 
to Sodd 3 ', therefore, that credit is due 
for being the first to envisage the 
situation correctly from the modem 
standpoint, for in 1913 he suggested 
“that each knomi element may be a 
group of non-separable elements occu- 
jiying the same place [in the periodic 
table], the atomic weight not being a 
real constant, but a mean value, of 
much less fundamental interest than 
has been hitherto supposed. Although 
. . . matter is even more complex than 
chemical analj'sis has lieen able to 
reveal . . . the problem of atomic con- 
stitution may be more simple than has 
been supposed from the lack of simple 
numerical relat ions between the atomic 
weight.^.” 

8.45. In this latter conjecture Soddy 
wa.s, of course, correct; while there 
e.xistcd the possibilitj'- of fractional 
jitotnic weights, there could be no 
simple thcoiy of nuclear structure. 
Tijc discovery of the whole number 
rule removed, in the words of Aston, 
“the onl\» serious objection to a uni- 
tary thcorj' of matter.” Tlic fact that 
.‘ill imc}c.ar niasscs are approximately 
integral is in complete accord noth the 
view that atomic nuclei are built up 
of neutrons and protons which have 
masses very close to unitj’ on the 
r.tomic weight scale. As stated in 
f 8.13, the isotopc-s of a given element 
diiTer from one another by the number 
of neutrons in the nucleus; the isotopic 
.nto:nie weights should thus differ by 


189 

small integers, as is undoubtedly the 
case. It should be mentioned that al- 
though the masses of isotopes approxi- 
mate to whole numbers, or to the sum 
of the masses of their constituent neu- 
trons, protons and electrons, certain 
differences do exist; these differences, 
although small, are definite and of 
great significance as wall be seen in 
Chapter XII, 

The Isotopic Composition 
OP THE Elements 

8.46. In 1918, even before Aston had 
built his first mass spectrograph, A. J. 
Dempster in the United States had 
designed an instrument based on a 
somewhat different principle which will 
be described below. This instrument 
could be used to determine the rela- 
tive proportions, as w'ell as the masses, 
of the particles present, and with it 
Dempster examined the metals lithium, 
magnesium, potassium, calcium and 
zinc. Two years later, he reported that 
these elements, like many of the non- 
metals studied by Aston, consisted 
of mixtures of isotopes with atomic 
weights that were close to whole num- 
bers, 

8.47. Before the year 1921, there- 
fore, it had been established that sev- 
eral elements, with atomic weights 
ranging from 10 to 238, existed in 
isotopic forms, and that the phenome- 
non of isotopy was quite general over 
virtually the whole of the periodic 
table. Since that time the mass spectra 
of all the Icnown elements have been 
investigated and their isotopic compo- 
sitions have been determined.* The 
results for the nonradioactive elements 
are tabulated hete; the masses of the 
naturally occurring isotopes are given 


• Tiif 
rp.-c 


topf's of hydrogen, whon, nitrogen and oxygen were diFcovcred by means of 
u. ... 'ik'.ntified in the earlier mass .spectrographs because their faint 

'n ,• ’ ^ f" t of other substnnecs winch \Yere, or might have tK>en. present 

of later instrumeS^ of^^eater’ 



190 


Chap VIII 


Smcrcebock on Aiomlc Energy 


I90T0PE3 or TUB NONRWIOACTIVB ELEMENTS 



Atomic 



Atomic 


Element 

No 

laolopee 

Element 

No 

Isotopes 

Hydrogen 

1 

1,2 

Indium 

49 

113, 115* 

Helium 

2 

3, 4 i 

Tin 

50 

112, 114, 115, 118 

Lithium 

3 

6, 7 



117, 118, 119, 120 

Beryllium 

4 

9 ! 



122, 124 

Boron 

5 

10, 11 1 

Antimony 

51 

121, 123 

Carbon 

6 

12, 13 1 

Tellurium 

52 

120, 122, 123, 124, 

Nitrogen 

7 

14, 15 



125, 126, 128, 130 

Oxygen 

8 

16, 17, 18 

Iodine 

S3 

127 

Fluorine 

9 

19 

Xenon 

54 

124, 126, 128, 129, 

Neon 

10 

20, 21, 22 



130, 131, 132, 134, 

Sodium 

11 

23 



136 

Magnesium 

12 

24, 25, 26 1 

Cesium 

55 

133 

Aluminum 

13 

27 

Barium 

56 

130, 132, 134, 135, 

Silicon 

14 

28, 29, 30 



136, 137, 138 

Phosphorus 

15 

31 

Lanthanum 

57 

l3S,t 139 

Sulfur 

16 

32, 33, 34, 36 | 

Cenum 

58 

136, 138, 140, 142 

Chlorine 

17 

36. 37 ' 

Praseodymium 

59 

141 

Argon 

18 

36, 38, 40 

Neodymium 

60 

142, 143, 144, U5, 

Potassium 

19 

39, 40,* 41 1 



146, 148, 150* 

Calcium 

20 

40, 42, 43, 46, 48 

Promethium 

61 


Scandium 

21 

45 1 

Samarium 

62 

144, 147, 148, 149, 

Titamura 

22 

46, 47, 48, 49, 60 



150, 162,* 164 

Vanadium 

23 

60, t 51 

Europium 

63 

151, 153 

Chromium 

24 

50, 52, 53, 54 1 

Gadolinium 

64 

152, 164, 165, 156 

Afangsnese 

25 

55 , 



J57, 168, 160 

Iron 

2b 

54, 56. 57, 58 ! 

Terbium 

65 

159 

Cobalt 

27 

59 

Dysprosium 

66 

156, 158, 160, 161, 

Nickel 

28 

38, 60. 61, 62, 64 



162, 163, 164 

Copper 

29 

63, 65 1 

Holimum 

67 

165 

Zme 

30 

64 66, 67, 68, 70 

Erbium 

68 

162, 164, 166, 167, 

Gallium 

31 

69, 71 



16S, 170 

Germanium 

32 

rO, 72, 73, 74, 76 

Thulium 

69 

169 

Arsenic 

33 

75 

Ytterbium 

70 

168, 170, 171, 172, 

Selemum 

34 

74. 76, 77, 78, 80, 82 



173, 174, 176 

Bromine 

35 

79, 81 

Lutetium 

71 

176, 176* 

Krypton 

36 

78, 80, 82, 83, 84, 86 

Hafnium 

72 

174, 176, 177, 178 

Rubidium 

37 

85, 87* 



179, 180 

Strontium 

38 

84, 86, 87, 88 

Tantalum 

73 

181 

Yttrium 

39 

89 

Tungsten 

74 

180, 182, 183, 184, 

Zirconium 

40 

90, 91, 92, 94, 96 



186 

Columbium 

41 

93 

Rhenium 

75 

185, 187* 

Molybdenum 

42 

92, 94, 95, 96, 97, 98, 

Osmium 

76 

184, 186, 187, 188, 



100 



189, 190, 192 

Technetium 

43 



Indium 

77 

191, 193 

Ruthemum 

44 

96, 98, 99, 100, 101, 

Platinum 

78 

190, 192, 194, 195, 



102, 104 



196, 198 

Rhodium 

45 

103 

Gold 

79 

197 

Palladium 

46 

102, 104, 105, 106, 

Mercury 

80 

198, 198, 199, 200, 



108, 110 



201, 202, 204 

Silver 

47 

107, 109 

ThaUium 

81 

203, 205 

Cadmium 

48 

106, 108, 110, 111, 

Lead 

82 

204, 206, 207, 208 



112, 113, 114, 116 

Bismuth 

83 

209 


• Radioactive 
t Probably radioactive 


Isotopes 


191 


to tlio nearest integers, on the atomic 
weigiit scale. It is seen that only 
twenty-one elements, about one fourth 
of the whole, are single species; all 
the others consist of two or more ipo- 
fopc.s of difTerent masses, tin having 
as many ns ten isotopes. 

8.48. The accompanying table lists 
over 280 isotopic forms of stable ele- 
ments* and if to these arc added the 
•10 or .so radioacti\'e isotopes, it is seen 
that a total of more than 320 isotopic 
species c.xist in naUire. In addition 
there have been obtained in recent 
years several Inindred which do not 
occur natural!}-, so that at the present 
time there have been identihed more 
than a thousand forms of the ninety- 
eight known elements. 

8.49. With the incrciising complex- 

ity of the .subject there has been some 
feeling that a more precise terminologj’’ 
wfis desirable. Con.scciuently, in 1947, 
T. r. Kolunan, in the United States, 
])roposed the term imejide for a species 
of atom characterized by the constitu- 
tion of its nucleus, th.at is, by the 
mimbens of neutrons and protons it 
contains. Thus, the species whose 
mnssc.s are given in the table might 
be referred to a.s naturally occurring, 
.stable nuclides. Similarly, cverj- radio- 
olcmcni is a radioactive nuclide or 
radionuclide. An isotope would then 
l>r one of a group of two or more 
nuclides having the .same number of 
protons or, in other words, liaving the 
Siime atomic number. An element like 
nuorine, of which only one species 
exists in nature, would then be .s.aid to 
fonn a .migle stable nuclide, rather 
than a .single .•.table isotope, .^ince the 
word i.-^^itope seem.^ to imply more than 
ojic oceupying the same place in 

tliO perioKiic system. 


Mass Spectrographs 

8.60. Following upon the pioneering 
work of Aston and of Dempster, which 
has been mentioned above, a great deal 
has been done with the object of im- 
proving the accuracy and simplifying 
the operation of the mass spectro- 
graph. Both Aston and Dempster made 
important contributions in this con- 
nection, as also have several- other 
physicists, notably K. T. Bainbridge, 
W. Bleakney, E. B. Jordan and A. 0, 
Nier in the United States, and J. 
Mattauch in Austria, Of the many in- 
struments that have been constructed 
for determining the masses of posi- 
tively charged particles, twm only will 
be described here. They have been 
selected because they embody some- 
w'hat different characteristics which 
are of special interest. 

8.51, In one form of Dempster’s 
mass spectrograph, the element being 
studied is vaporized by heating it elec- 
trically, and the atoms in the vapor are 
then ionized by bombardment with 
electrons emitted from a hot filament. 
The positively charged ions so pro- 
duced emerge from a hole in the plate 
Pi (Fig. 8.4), and they are then ac- 


lOH SOURCE TO PUMP TO METER 



Fk:. 8.4. Dempster’s mass 8i>ectrograph 
(direction focusing). 



these ".RtaWc" elements c,xhibit feeble 
Lu(I76), and Re(187); also, pos- 
be radioactive. 



194 


Sourc^oh on AUtmxc Energy 


topes were exactly integral or whether 
there were small deviations from, whole 
number values Consequently, he pro- 
ceeded to construct a new instrument 
capable of greater precision, and his 
second mass spectroscope, completed 
about 1925, was capable of giving re- 
sults accurate to about one part in ten 
thousand With this apparatus, Aston 
showed that the masses of the indi- 
vidual isotopes (nuclides) on the atomic 
weight scale, commonly known as the 
isotopic weights, actually differed from 
whole numbers, although the differ- 
ences were very small Later work by 
Aston and others has confirmed this 
discovery, some isotopic weights are 
slightly less than integers and others 
are somewhat greater but, ivith the 
exception of the heavy radioactive ele- 
ments, the maximum deviation is about 
0 06 atomic weight unit, most of the 
differences being considerably smaller 
The integer nearest the isotopic weight, 
which is commonly used to identify 
the isotope, Aston called the mass 
number * The table m § 8 47 thus 


Chap vni 

fortunately, the results so obtjuned are 
not exactly equivalent to those based 
on the ordinary chemical atomic weight 
scale The reason for the discrepancy 
is that on the latter scale the figure 
16 0000 is associated ivith ordinary 
atmospheric oxygen, which is actu- 
ally a mixture of isotopes, ivhereas oa 
the mass spectrographic, or physical, 
atomic weight scale this is taken as 
the isotopic weight of the single, most 
abundant isotope 

8 60 The relationship between the 
two scales may be determined m the 
following manner Atmospheric oxy 
gen consists of 99 76 per cent of the 
isotope of mass 16 0000, together with 
004 per cent of the one of mass 
27 0045, and 0 20 per cent of that of 
mass 18 0049, all on the physical atomic 
weight scale The weighted mean of 
these values is 16 0044, so that this is 
the atomic weight of atmospheric oxy- 
gen on the physical scale, as compared 
with the postulated value of 16 0000 
on the chemical scale It follows, 
therefore, that 


Physical Atomic Weight _ 16 0044 
Chemical Atomic Weight 16 0000 


gives the mass numbers of the known 
stable nuclides of the elements 
8 69 It will be seen from this table 
ihai csryges cvaststs oi three lacAopes 
ivith the mass numbers of 16, 17 and 
18, respectively Of these, the first one 
13 by far the most abundant since it 
constitutes 99 76 per cent of atmos- 
pheric oxygen In the determination 
of isotopic weights by the mass spec- 
trograph it 13 the invariable practice 
to take as the standard of corapanson 
the value of 16 0000 for the weight of 
this common isotope of oxygen Un- 
• While the atomic number of any epecies «] 
the mass number givea the total number of prot 
(§ 4 35) The present wnter has consequentiy 
of mass number 


and hence isotopic weights obtained by 
means of the mass spectrograph must 
be divided by 1 00027 m order to con- 
the iresvitts te the atomic- 

weight scale Althou^ it is the in- 
variable practice in nuclear studies to 
employ isotopic wei^ts on the physi- 
cal scale, there are occasions when it is 
of interest to compare mass spectro- 
graphic results with those obtained by 
chemical methods, m such mstances 
the conversion factor is used 

8 61 In addition to giving the atomic 
weights of the isotopic constituents of 
iresents the number of protons m the nucleus 
ons and neutrons i e , the number of nucWM 
proposed the name nucleon number, in place 



Isoifypes 


195 


an clement, their relative amounts can 
also be obtained, as mentioned earlier, 
by means of the mass spectrograph. 
In fact, one of the most important uses 
of the mass spectrograph at present is 
for the quantitative analysis of both 
naturally occurring and partially sepa- 
rated mixtures of isotopic substances. 
The proportions of the various isotopes 
fire referred to as the abundance ratios 
or the relative abundances or, in brief, 
ns Ibc abundances. The values are 
URially expressed as percentages, so 
that the abundances of the three iso- 
topc.s of oxygen, as recorded above, are 
99.70, 0.01 and 0.20 per cent, respec- 
tively. The atomic weights and the 
relative abundances of the isotopes of 
some common elements, as they occur 
iti nature, arc quoted in the accom- 
panying table. 


l.ROToric Wr.ioiiTS axd Ahuxbances 



iTo-rs 

Isoln-pic 

Ahnn- 

dancr 

ntniirnl 

Kumher 

Weight 

Per Cent 

liyibogi-t) . , . 

1 

1.008123 

99.9S 


2 

2.0M70S 

0.02 

boron 

.. 10 

10.01G77 

18.83 


11 

11.01244 

81.17 

C;4r!>on 

.. 12 

12.00382 

OS.fl 


13 

13.00751 

1.1 

Kiiropfu. . 

. . 14 

14.00751 

99.62 


15 

15.OO4S0 

0.38 

O.wgen 

.. 16 

16.00000 

99.70 


17 

17.00150 

0.01 


18 

180049 

0.20 

Siilfiir 

. . 32 

S1.9S09 

95.06 


33 

32.9800 

0.74 


31 

'33.9771 

4.18 

Chlorine*. , , . 

. . 35 

34.97FG7 

75.4 


37 

30.97750 

24.0 



.. fC 

62.956 

69.09 


05 

61.955 

30.91 


8,62, It of i!it»'’rest to compare the 
aiomic weight^' of eleinents as deter- 


mined bj’’ chemical methods with the 
mean values derived from mass spec- 
trograph results. For example, boron, 
as it occurs in nature, consists of two 
isotopes of atomic weights 10.0168 and 
11.0124, whose abundances are 18.83 
and 81.17 per cent, respectively. The 
weighted mean of these two physical 
isotopic weights is 10.825, and upon 
dividing by the conversion factor 
1.00027, the atomic weight of ordinary 
boron is found to be 10.822 on the 
chemical scale; this may be compared 
witlr the accepted value of 10.82 ob- 
tained by chemical methods, as out- 
lined in Chapter I. There is little 
doubt that at the present time the 
mass spectrograph provides the most 
reliable general method for the deter- 
mination of atomic weights. The val- 
ues obtained in this manner are accu- 
rate to better than one part in ten 
thousand, a precision wliich is rarely 
obtainable in chemical analysis. In 
several cases the previously adopted 
atomic weights have been proved to 
be incorrect as a result of studies with 
the mass spectrograph. During the 
1920s, for example, the chemical atomic 
weight of boron was quoted as 10.90, 
but the isotopic analysis indicated an 
appreciably lower value. Subsequent 
redetermination by improved chemical 
methods gave 10.82, in agreement with 
the mass spectrograph value 10.822, 
as stated above. 

8.63. For the majority of elements 
studied the relative abundances of 
their isotopes have been found to be 
independent of the source of the ma- 
terial. In some instances, however, 
variations have been detected. Lead, 
^ociated with radioactive minerals, 
is an outstanding example; as indicated 
in § 8.24, lead from uranium minerals 
contains more of the 206 isotope, 
whereas the thorium minerals have 
more of the 208 Isotope, However, 



196 


Sourcebook on Atomic Energy Chav VIII 


lead denved from apparently non- 
radioactive sources also exhibits slight 
differences in isotopic composition 
The same is true of hydrogen, carbon, 
oxygen and, possibly, chlorine, the 
significance of some of these variations 
will be considered later 

Heavy Hydrogen Deuterium 
8 64 For many reasons, one of the 
most notable of the stable isotopes is 
that of hjdrogen, its discovery, m 
1931, marked an important advance 
in understanding the chemical behav- 
ior of isotopes in general In 1920, both 
W D Harkins and E Rutherford, 
whose speculations concerning the neu- 
tron were mentioned m § 2 109, con- 
sidered the possibility that there mij^t 
exist a form of hydrogen u ith a mass 
approximately twice that of ordinary 
hydrogen Subsequently, other scien- 
tists argued that such an isotope was to 
be expected to fit in with the mass 
regularities exhibited by the known 
isotopes of other elements of low atomic 
weight Houever, as early as J919, 
0 Stem and M Volmer, in Germany, 
had sought, unsuccessfully, to detect 
the presence of a heavier isotope in 
ordinary hydrogen m order to deter- 
mme ^^hether the departure of the 
atomic u eight from exactly unity might 
be accounted for in this maimer They 
tnea' to 6nng about a partial sepa 
ration of the possible isotopes by Ef- 
fusion, the procedure by which Aston 
had been successful with neon (§ 8 37), 
but they were unable to detect any 
change of density Although it is now 
known that this failure was due to 
faulty expenmeiital technique, it served 
the purpose of discouraging others 
from seeking for an isotope, the exist- 
ence of vhichxvas in doubt It may be 
mentioned that the earlier mass spec- 
trographs were unable to shed any li^t 
on the problem, because %vith hyEogen 


m the apparatus there was invanably 
a Ime of mass approximately 2, due to 
molecular hydrogen (Hj), which could 
not be distinguished from that due to 
the isotopic atom of similar mass 
8 66 "^en, m 1927, Aston reported 
on the isotopic composition of hydro- 
gen as determined by the mass spectro* 
graph, he stated that it consisted of a 
single species of atomic weight 1 00778, 
apparently m excellent agreement ivith 
the chemical atomic weight 1 00777 
accepted at that time The discovery, 
two years later, by P W Giauque and 
H L Johnston, m the United States, 
that atmospheric oxygen is a mixture 
of three isotopes, showed that (phya 
cal) atomic weights obtamed by the 
mass spectrograph could not be iden- 
tical with the chemical values, as 
explained above By making the ap- 
propnate conversion of Aston’s mass* 
spectrograpbic atomic weight to the 
chemical scale, it would then become 
1 00751, as compared with 1 00777 de- 
termined by chemical methods The 
' difference between these tivo values 
' was appreciably greater than could be 
accounted for by the possible expen- 
mental errors, and m 1931 R T Birge 
and D H Menzel, m the United 
States, suggested it might be due to the 
presence in ordinary hydrogen of about 
one part in 4500 of a heavier isotope, 
concerning the existence of winch tdere 
had been much speculation, as stated 
above The lover result obtamed by 
the mass spectrograph would then be 
the atomic v eight of the lighter iso- 
tope, while that derived by chemical 
methods would be the weighted mean 
value for both isotopes normally pres- 
ent in hydrogen 

8 66 Encouraged by the calcula- 
tions based on the difference in atomic 
weights, and also by the fact that a 
hydrogen isotope of mass 2 was re- 
quired to complete a regular arrange' 



Isotopes 19 < 


ment of ‘the known isotopes, the Amer- 
ican scientisUs H. C. Urey, F. G. 
Brickwedde and G, Murphy set 
out in 1931 to make a thorough search 
for this isotope. Realizing that an iso- 
tope present to the extent of about one 
part in five thousand w'ould be difficult 
to detect, Brickwedde, at the U . S. Na- 
tional Bureau of Standards, evaporated 
4 liters of liquid hydrogen down to 
about 1 cc., since calculations had 
shorni that the heavier isotope, if pres- 
ent, would concentrate in the residue. 
An examination of the optical spec- 
trum* of this residue, by Urey and 
Jtfurphy at Columbia University, ex- 
hibited verj’ clearly a line in the precise 
jiosition required for an isotope of hy- 
drogen with a mass very close to 2 on 
the atomic weight scale. 

8.67. Subsequently, a careful study 
showed the same line to be present, 
although verj' much fainter, in the 
spectrum of ordinaiy hydrogen. Thus, 
definite proof was obtained of the ex- 
istence of a heavier isotope of hydro- 
gen. The concentration of this isotope 
by the distillation of liquid hydrogen 
was verified by a number of scientists 
in Europe; and further confirmation 
of its presence was obtained shortly 
afterward in the United States, when 
IV. Bleakncy found that the appropri- 
ate line could be detected in the mass 
sjK'cirograph, and K. T. Bainbridge 
defennined the isotopic mass. 

8.68. Soon after the discover)’ of .the 
heavier isotope of hydrogen, Urey, one 
ofits discoverers, together with E. W. 
Ma.'ihbum, of the U. S. National Bu- 
ix’.au of Standards, thought that a par- 
tial separation of the isotopes might be 
achieved by the electrolysis of water,! 


that is to say, by decomposing water 
by means of an electric current. W'liile 
the e.xperiments to test this possibility 
were still in progress, a sample of w’ater 
obtained from industrial electrolytic 
cells, which had been used for the 
production of hydrogen and oxygen, 
was examined by E. R. Smith, at 
Washburn’s suggestion, and found to 
have a density appreciably higher than 
that of ordinary water. This difference 
was attributed to the presence in the 
former of an excess, above the normal 
proportion, of water molecules con- 
taining the heavier hydrogen isotope. 

8.69. It thus appeared that upon the 
electrolysis of water — actually an aque- 
ous solution was used — the lighter iso- 
tope of hydrogen is evolved more 
readily than the heavier one, so that 
the latter accumulates in the residual 
water. Consequently, by prolonged 
electrolysis, it might be possible to 
concentrate the hea^^er isotope. Tins 
w'as actually achieved in 1933 by G. N. 
Lends and his collaborators at the Uni- 
versity of California; by continued 
electrolysis of a large quantity of water 
from an old commercial electrolytic 
cell, they obtained ultimately a small 
residue in which almost all of the 
hydrogen was in the form of the heavier 
isotope. Other scientists, in the United 
States and elsewhere, soon followed up 
tlus work, using larger quantities of 
electroljde and improved procedures, 
so that appreciable amounts of the 
isotope u’ere isolated. Since ordinar}’ 
hydrogen consists almost entirely of 
the lighter isotopic species, it meant 
that both isotopes were now available 
for e.\perimental purposes in an almost 
pure state. 


cncrg.v levels and %vhicli arc studied by the 
course, not be confu.=cd with mass spectra. The optical 

J. i”S feSsSte.’’-'' by 



198 Sourcehook on Atomic Energy Chap VIII 

8 70 Because the atomic weights of 8 72 Pnor to the discovery and 
the two isotopes of hydrogen are in the isolation of deuterium, it was generally 
approxunate ratio of 2 to 1, which is believed that the isotopes of a given 
greatly m excess of that for any other element could not be separated by 
element, the otherwise small differ- chemical methods since they had iden 
ences m physical and chemical proper- tical chemical properties (§ 8 7) IVhile 
ties of isotopes are so much accentuated it is true that isotopes do undergo the 
that it was considered desirable to same chemical reactions expenments 
ascnbe different names to these jso with deuterium drew attention to the 
topes The name deutmum* was sug- fact that the different isotopes react at 
gested for the heavier isotope by its different rates The difference is negli 
discoverers, and this together with the gible for the isotopic forms of the 
symbol D, has been wndely adopted heavier elements but for elements of 
The nucleus of the deuterium atom is low atomic weight, and particularly 
called a deuteron by^ analogy with the for hydrogen, the effects are very 
term proton for the nucleus of the significant 

lighter isotope (§ 2 64) The deuteron 8 73 The molecules of the lighter 
with a positive charge of one unit and a isotope of hydrogen (Hj), in the gaseous 
mass of approximately two units on form, undergo what is known as an 
the atomic weight scale is evidently exchange reaction v\ith liquid heavy 
made up of a proton and a neutron watei (DiO), the two isotopic forms of 

8 71 The name hydrogen and the hydrogen exchanging places with one 
symbol H are used both for the lighter another, thus, from left to right, 
isotope and for the naturally occurring 

mixture which contains 99 98 per cent H» (p) -h DjO (f) D: (g) + HiO (1) 
of this form Where a distinction is 

necessary the expression light hy- where the symbols (7 and f indicate gas 
drogen is used as against heavy and liquid, respectively t The reverse 
hydrogen for deuterium, the heavier reaction, between deuterium gas (Di) 
isotope Ordinary water has the for and light water (H2O) is also possible 
mula H2O whereas heavy water as it js as is to be expected if isotopes exhibit 
familiarly called in which all the hy- similar chemical behavior, thus, 
drogen consists of the heavy form, has 

the scientific name of deuterium oxide H? (g) + D2O (Z) *— Dj (g) -f HjO (Z) 
and 13 represented by D O The den- 
sity of heavy water is 1 lOSascompared from right to left The interesting 
with 1 000 gram per cc for ordinary point is that, provided the concentra 
water it freezes at 3 82°C and boils at tions of the reacting substances are the 
101 42*0, the corresponding temper- same in both cases, the latter reaction 
atures for normal water being 0®C and takes place about three times as fast 
100°C The differences m the physical as the former, so that if the equilibrium 
properties of bght and heavy water are 

thus quite appreciable H* (g) -f- D2O (1) ^ Dz (g) 4- HjO (Z) 

* From the Greek, deuteroi (second) The analogous term protium (from proloa, first) was 
suggested for the lighter isotope but this luta not come into general use Rutherford (1932) 
Mggested the names diplogen and haplogen for the two isotopes, from the Greek combining 
lOTTta dipJo (double) and kaplc (single) with tiie ^mbok D ana H respectively the names 
with limited acceptance and have now been m^arded 

7 The reaction actually also involves Uie uitennediate isotopic forms HDO and HD, but 
for the sake of simplicity they wiU be omitted from consideration here 


Isotopes 


199 


3 H establif'-hed between the isotopic 
forms of hydrogen gas and of liquid 
wafer, tlie Kul>slonccs on the left-hand 
side will be favored over those on the 
right-hand side. As a rc.sult, the ratio 
of dontcriuin to hydrogen in the liquid 
i.s found to be approximately three 
firne.s as great as in the gas. If the 
si)ccific rates* of the two isotopic ex- 
change reactions had been identical, 


the relative proportions of the isotopes 
would have been the same in both 
gaseous and liquid phases. The fore- 
going reaction has been chosen for 
consideration because it has been uti- 
lized, as will be seen shortly, for the 
large-scale concentration of deuterium, 
but other chemical processes exhibit 
similar beha\dor (§ 8.110 et seq.). 


THE SEPARATION OF ISOTOPES 


Tnr; Sni’AnATioN Factor 

8.74. Materials enriched in partic- 
ular isotopic forms of certain elements 
Imve found numerous applications, as 
will be apparent in later chapters. 
Consequently, considerable interest at- 
taches to the subject of the separation 
of i.sotopc.s. In the twenty or so years 
iminediatoly following the first devcl- 
Qjimont of the concept of isotope.s, par- 
tial concentrations had been achieved 
of the isotopes of a number of non- 
radio.'ietive elements, .such as neon, 
chlorine, mercury, zinc and pottissium. 
The results were, however, not spec- 
tacular, .and their main purpo.se was 
to provide confirmatory evidence for 
the existence of isotope.s. The notable 
success achieved in the concentration 
of deuterium, in spite of its verj' small 
.‘tbundance in ordinary hydrogen, and 
the useful scientific applications which 
wore found for it , msultcd in a . revival 
of inleiTst in the general problem of the 
separatiuu of i.^otope.s. This interest 
w.'us .‘-tiinulated by the necessity for 
oidnining uninium (uiriehed in the 23.0 
for the wartime atomic energ},’ 
prujeei (Chapter XIV), with the re- 


sult that, in the words of H. G. Urey, 
who has himself contributed largely to 
the subject, “it is [now] possible to 
separate the isotopes of an^' element, 
though the expense involved in certain 
processes is still greater than may be 
warranted by the particular objective 
sought.” 

8.76. The extent to which separation 
of isotopes is, or can be, achieved in a 
particular process is conveniently rep- 
resented by means of the separation 
factor, defined as the ratio of the abun- 
dance of a given isotope in the enriched 
stale to that in the initial state. For 
example, if an isotopic mixture con- 
tains a fraction (or percentage) / of a 
given isotope before treatment,! and 
f is the fraction (or percentage) pres- 
ent in the system after treatment, the 
separation factor s for this particular 
process is given by 



The larger the value of s in comparison 
with unity the more efficient is the 
Fppanvtion. If it Is only .slightly greater 


*' 11 , 
Tbr* f,c5 


of a rhi-niiraS n-\cljor) depends on the eoncentrntion of the reactinc; substances. 
v'S'.ivc implu*? tliat the concentrations arc the same (unilv) in each ease so 


Use rx-;!h>= nrx- comparahle «ilh one another. 



eompo': 


(unity) in each ca.se, so 

reinaininc after removal of the enriched 
lion factor is a«ually dose to unity, the 
~ material Ijcforc treatment. 



200 Sourcebook on 

than unity, the &\tent of separation is 
small, and many successive stages may 
be necessary to obtain an appreciable 
concentration Of the desired isotope 
If the separation factor is s in each 
stage, the overall separation factor for 
n stages is s”, which can become quite 
appreciable, if n is sufficiently lar^, 
even though s may be close to unity 
(§8 84) 

The Gaseous Diffusion Method 
8 76 Histoncally, the first success- 
ful method for the enrichment of iso- 
topes, and one which is still of pnme 
importance, made use of the different 
rates of diffusion of gases through a 
porous barrier * Since the early years 
of the nineteenth century, it has been 
known that the rate of diffusion of a 
gas IS inversely proportional to the 
square root of its density The reason 
IS that, at the same temperature, the 
molecules of a light gas move, on the 
average, ^vith a higher speed than do 
those of a heavier gas It m os seen m 
§ 1 33 that the gas density is directly 
related to the molecular v eight of the 
substance, and so it follows that the 
rate of diffusion is inversely propor- 
tional to the square root of the molec- 
ular weight Thus, a gas of lower 
molecular weight will pass throu^ a 
particular porous barrier faster than 
one of higher molecular weight Hence, 
m a imxitoe in' tNto isutopic moibcoiles, 
those contaming the hghter isotope will 
diffuse more rapidly than the heavier 
species This fact was utilized m 1913 
by F W Aston to obtain a partial 
separation of the isotopes of neon, as 
mentioned earlier (§ 8 37), and m 1921 
W D Harkins, in the United States, 
reported slight enrichment of the iso- 
topes of chlorme by diffusion of by- 


Aiomic Energy Chap VIll 

drogen chloride gas through pipe clay 
8 77. If M\ IS the molecular weight 
of the form containing the hghter iso- 
tope, and Ml is that of the form with 
the heaMer isotope, the ideal sepa- 
ration factor for diffusion is repre- 
sented by 



Actually this is a maximum value 
which can be realized only at the 
beginning of the process for, as diffu 
Sion continues, the gas is being steadily 
impovenshed of the hghter, more rap- 
idly diffusing, constituent As a result, 
the dtffusaic, that is, the gas passing 
through the bamer, contams decreas- 
ing proportions of the latter If diffu- 
sion were allowed to proceed long 
enough, the composition of the gas 
would, of course, be the same on both 
sides of the barrier, and there would be 
no separation of the isotopes In prac- 
tice, therefore, there has to be a com- 
promise between the quantity of gas 
permitted to diffuse and the resultant 
separation factor, this is achieved by 
alioivmg about half of the gas to pass 
through the bamer 

8 78 It can be seen from equation 
(8 11) that the larger the ratio of the 
molecular weights of the two isotopic 
tke hwU he the sef&xz.- 

tion factor, and hence the efficiency of 
separation by diffusion The most far 
vorable case for naturally occurring 
isotopes IS that of hydrogen gas where 
the molecular weights Mi and Mi are 
approximately 2 and 4, respectively, so 
that the maximum (initial) separation 
factor is V 2 , 1 e , 1 414 For the two 
most abundant isotopes of neon (mass 


• The passage of gas through fine pores, Braall in comparison with the distance between 
the molecules, is properly called ejfu«on, rather than diffusion However, the latter terra is 
almost invanably used m the present connectian and so it will be employed here 


Isotopes 


numbers 20 and 22) this factor is 1.049, 
and for those of chlorine (mass num- 
bers 35 and 37), using hydrogen cWo- 
ride as the diffusing gas, it is 1.028. It 
is apparent, therefore, that the extent 
of isotopic enrichment by diffusion de- 
creases rapidly with increasing atomic 
weight of the clement whose isotopes 
are to be separated. 

8.79, In order to improve the effi- 
ciency of the diffusion process, G. 
Hertz of Germany introduced in 1932 
the “cascade” principle with recycling, 
which may be illustrated by means of 
the diagram in Fig. 8.6. A number of 
units are shown, each containing a 


201 

recycled. In this way, the gas moving 
to the left from one unit to the next be- 
comes increasingb' richer in the lighter 
isotope, while that traveling to the 
riglit contains an increasing proportion 
of the heavier species; thus, a kind of 
fractionation process is taking place. 

8.80. In his work, Hertz used a 
closed system, so that the gas contain- 
ing more of the lighter isotope collected 
in a vessel at one end, and that en- 
riched in the heavier isotope accumu- 
lated at the other end. It is possible, 
how'ever, to imagine a somewhat simi- 
lar cascade of diffusion barriers in 
which gas is fed continuously into one 



PUMP PUMP 


Fio, 8.0. Diagrnmnifttic representation of cascade principle for sep- 
aration of i.sotopes by diffusion. 


porous diffusion barrier reprc.sented l>y 
a broken lino. Consider the unit B: the 
g!is enters from the right, and the 
arraiiganent of pump.s permits .about 
one half to diffuse tlirough the barrier. 
The diffusale, which is riclicr in the 
lighter isotope, tlicn p.as.''e.s into unit 
A ; here it undcrg()e.s further diffusion, 
the diffusatc containing a .still higher 
!)roi)ortion of this isotope. Turning nt- 
lentmn once again to B, it will be seen 
th.at the g!r.s. which has not diffused, 
and whicli is con.«equcntly .somewhat 
impoveri''bp<l in the lighter .'■pecics, is 
reeyelfv}; ihjit is to say, it retum.s to 
unit C, when' it join.s the diffusate from 
^'suiting gas then undergoes 
dijiusiO!) in C, the diffusate going on to 
igwhilethe remainder returns ioD tobe 


of the intermediate units, and is drawn 
off steadily at the two extremes. At 
one end, the left-hand in Fig. 8.6, the 
gas hiis a greater abundance of the 
ligliter isotope and at the other end a 
larger proportion of the heavier isotope 
than does the feed gas. 

8.81. Utilizing some form of the dif- 
fusion method, a number of investi- 
gators, both in Europe and America, 
achieved partial separation of the iso- 
topes of hydrogen, carbon (in methane), 
nitrogen, oxygen, neon and argon. But 
the most remarkable application of the 
diffusion procedure is the concentra- 
tion on a large scale of the 235 isotope 
of uranium, present to the extent of 
0.72 per cent in ordinary uranium. 
The procc.S3 wa.s developed in the 




202 Sourcebook on Atomic Energy Chap YIU 

United States during World War II, mixture of two isotopic forms, with 
and has been in successful operation molecular weights of 235 + 6 X 19 
since the spring of 1945 In his report i e , 349, and 238 + 6 X 19, i e , 352, 
on Atomic Energy for Military Pur- respectivelyjhencethf* maximum sepa- 
poses, written m that year, H D ration factor is given by equation 
Smyth refers to this as “a notable (8 11) as 
achievement,” although a full realiza- 
tion of the problems solved and the ^ _ 1^2 _ ^ 

difficulties overcome, warrant it being V 349 

descnbed as a stupendous feat * 

8 82 In considering the possibility Close as this is to unity, the actual 
of separating the isotopes of uranium, separation factor, which takes into ac 
it should be noted that uranium is a count the fact that an appreciable 
solid metal, and so it is first necessary proportion, usually about one half, of 
to choose a compound of uranium that the gas must be allowed to diffuse 
can be readily converted into a gas. A through the barrier, is even closer 
fairly obvious choice is uranium hexa- The first experimental measurements 
fluonde UFe, for although it is a solid made by E T Booth, H C Paxton 
at ordinary temperatures, it is easily and C B Slade at Columbia Univer- 
vaporized An important advantage of sity, indicated a value of about 1 0014, 
the use of a compound of fluorine for which would appear to bo so near to 
this purpose is that this element con- unitj as to be of no use for the practical 
sists of a single nuclide, as can be seen separation of the uramum isotopes 
from the table in § 8 47 Consequently, However, the situation was not alto- 
the course of the diffusion process wifi gether hopeless, as the following con- 
be determined only by the uranium siderations wll show 
isotopes, and not by the fluonne On 8 84 Since the proportion of ura- 
the other hand uranium hexafluoride mum 235 is raised by a factor of only 
has the great disadvantage of being a 1 0014 in each diffusion stage, it i3 
highly reactive and corrosive gas, so clearly necessary to increase the num- 
that special materials would have to be ber of stages in cascade sufficiently to 
used for pipes, vessels, pumps and even obtain the desired ennehment If there 
for lubrication purposes are n successive stages, the overall 

8 83 As found in nature, uramum separation factor wiU then be (1 0014)", 
contains three isotopic forms with mass and a simple calculation shows that a 
numbers of 234, 235 and 238 ,t the ten-fold ennehment of the lighter iso- 
proportion of the 234 isotope is only tope could be achieved m about 1800 
0 006 per cent, so that its presence may Stages In order to mcrease the abun- 
be Ignored The uranium hexafluoride dance of uranium-235 from its normal 
may thus be regarded as essentially a value of 0 72 ^er cent to 99 per cent, n 

• The report on Atomic Energy for Military Ptirposvs subtitled The Official Report on the 
Developmenl of the Atomic Bomb under the Auepicea of the United Slates Government 1940~S9io, 
often referred to as the Smyth Report gives a full account of the development of this and 
other procedures which were considered for the separation of uramum 235 The discussion 
m this book will therefore be restricted to the essenUal principles required for an understand 
ing of the more important methods used 

t The 238 and 234 isotopes are uramum I and II respectively, of the uranium disintegra- 
tion series while the 235 isotope is actinomranium the parent or the actnuum senes (Chap- 

I ter V) In the chemical preparation of uramum hexafluoride, or other compounds, the highly 
radioactive disintegration products are lar^y removed 



Isofopes 


203 


would have to be about 4000. 'Ihus, 
using ordinary urnnivini hexafluoride as 
the process gas, a cascade of something 
like 4000 diffusion stages would be re- 
quired to yield a product in which the 
uranium was almost entirel}’ in the 
form of the lighter isotope. These 
numbers, although very large, did not 
appear to be ])eyond the bounds of 
Ijossibility when the project was under 
consideration. 


barriers could be made was by etching 
a thin sheet of silver-zinc alloy by 
means of hydrochloric acid. The acid 
would then dissolve out some of the 
zinc atoms, leaving a large number of 
submicroscopic holes in the sheet of 
metal. 

8.86. So far no indication has been 
given of the quantity of enriched ma- 
terial that can be obtained by means of 
the diffusion cascade. Actually, this is 



V- ~ “ - s'A' I ri c:!e c 

.i' , 'I — — — — “ 


\ , 

Arv V 


L-. 

< fiw '.4 >. 


^ tiiL > _ J 

lC> A mt ^ A A 

/ £• £> £' t 

if // 

'd' 4/ if 

^ >»4* >i« 

., 1 . 


r.' iOt sr;« vr^ ^ tLi , 

“i 


(» .. If . J4 ff f. .. 4 t ... , t. (. • 

r,v» I s 

.it c , .7 










'.J 


et 




Fro. 8,7, Part of the plant for the separation of uranium-235 by gaseous ditfusion 

at Oak Ridge, Tenn. 


8.85. Tlie nature of the diffusion 
barrier merits .some attention. To ob- 
tain true diffusion, or rather effusion, 
which makes isotopic sejjaration pos- 
sible, it is necessarj’ that the pores 
should be less than one tenth the moan 
free path of tlic rnolcoule.s, that is, less 
than one tenth of the average distance 
a ps molecule travels before it collides 
v.ith another molecule. Calculations 
VcihhI on the kinetic theory of ga.'^cs 
show that at oulinarj- prcssure-s the 
holes in the barrier would have to be 
about millionth of a centimeter in 
diameter. One vay in uhich such 


quite small, for one of the disadvan- 
tages of the process is that it has to 
operate with gases, and to some extent 
at low pre.':suros. Consequently, the 
volume of the system is large, hut the 
output, in terms of weight, is com- 
paratively small. Thus, in a general 
review of the methods for separating 
isotopes, written at the end of 1939, 
Urey stated that in the lahoratorj' the 
“casoade-diffvision methods have trans- 
ports of about 1 cc. of gas per day.” 
For a Eiihstance of molecular weight 
about 350, this would mean approxi- 
m.aicly O.OIG gram per day, so that it 




204 


Sourcebook on Atomic Energy Chap YUJ 


would take about two xncmths of con- 
tinuous operation to obtain a single 
gram of the product It is obvious that 
for large-scale production, either the 
size of the vessels or the numbers of 
cascades, or both, would have to be 
very considerable 

8 87 “By 1942,” says the Smyth 
Report, “the theory of isotope sepa- 
ration by gaseous diffusion had b^n 
well worked out, and it became clear 
that a very large plant would be re- 
quired ” In the summer of 1943 con- 
stmction of a gaseous diffusion plant 
for the quantity production of en- 
nched uramum-235 was started at Oak 
Ridge, Tenn But it waa not until 
nearly two years later, after many 
perplexmg problems had been solved, 
that it came into full operation With 
Its thousands of miles of piping and 
hundreds of acres of diffusion banners, 
the plant is one of enormous size 
(Fig 8 7) It IS indeed a monument, 
m the words of the Smyth Report, to 
the “courage and persistence, as well 
as the scientific and technical ability,” 
of the physicists, chemists and engi- 
neers who were responsible for its 
planning, construction and operation 

The Electhomagnetic Method 

8 88 The electromagnetic method 
of isotopic separation is of special m- 
terest as it was the first to yield appre- 
ciable amounts of uranmm-235 for the 
wartime atomic energy project, al- 
though it IS no longer used for that 
purpose Because of its great con- 
vemence and adaptability for work on 
a moderate scale, however, the pro- 
cedure IS now being extensively em- 
ployed for the production of the sepa- 
rated isotopes of some forty stable 


elements for use m vanous research 
problems (Chapter XVI) 

8 89. The prmciple of the electro- 
magnetic method is essentially that of 
the mass spectrograph, in w^ch each 
isotopic species present m a stream of 
ions is bent through a different path 
by a suitable arrangement of electnc 
and magnetic fields (§ 8 51) If, m- 
stead of the photographic plate or 
other device used for detecting the 
positively charged ions, a number of 
small receivers are placed in the proper 
positions, the separate isotopes can be 
Collected * By usmg this method, 
which was suggested by F TV Astoa 
in 1919, the English physicists M L E 
Ohphant, E S Shire and B M Crow- 
ther succeeded, in 1934, m obtaming 
very small quantities — less than one 
tcn-milhonth part of a gram — of the 
separated isotopes of lithium m virtu- 
ally pure form Almost simultaneously, 
W R Smythe and his collaborators in 
the United States described an im- 
proved form of the apparatus, using 
the same principle, by means of ishich 
they weie able to separate appreciable 
amounts of the isotopes of several ele- 
ments 

8 90 Because the mass-spectro- 
graphic, or electromagnetic, method 
offered the advantage of efficient sepa- 
ration, even for isotopes of high atomic 
weight, it found application m certain 
instances where only minute amounts 
of the separated isotopes, provided 
they were in a fairly pure state, were 
adequate A case of particular mterest 
was that in which it was required to 
study the interaction of the isotopes of 
uranium wth neutrons By usmg the 
electromagnetic technique, A 0 Nier 
at the University of Minnesota, and 


• There is of course, an actual separation of isotopes m any mass spectrograph, but the 
amounts are extremely small, being sufficient merely to affect a photographic plate or to be 
recorded as an ion current 



Isotopes 


K. H. Kingdon and H, C. Pollock, at 
the General Electric Laboratories, 
Schenectady, New York, were able 
m 1940 to obtain sufficient uranium- 
235 to provide the answer to a \'ital 
problem in connection with the utiliza- ! 
tion of nuclear cnergj’ (§ 13.67). 

8.91. The advantage of the electro- 
magnetic method is that it is capable of 
giving large separation factors, but the 
quantitie.s of .separated isotopes col- 
lected are extremely small. Strong 
beams of positive ions which are to be 
deviated in the magnetic field are diffi- 
cult to produce and to manipulate, and 
the separation efficiency tends to di- 
mini.sh a.s tlie strength of the ion beam 
increases. Thus, an improvement in 
the .amount of material handled bj- the 
apparatus could be achieved only at 
the expense of its efficiency, so that 
there seemed little to be gained in this 
way. Consequently, when in 1940 the 
U. S. National Defense Research Coun- 
cil decided to investigate the feasibility 
of separating the isotopes of uranium, 
the electromagnetic method was re- 
jected as impractical. In this connec- 
tion, the Smyth Report states: "[H. D.] 
Smyth of Princeton had raised the 
question of possible large-scale sepa- 
ration of i-sotopes bj' electromagnetic 
means but had been told that it had 
been investigated and was considered 
impossible. Nevertlieless, Sm^dh and 
[E. 0.] Lawrence at a chance meeting 
in October 1941 discussed the problem 
and agreed that it might yet be pos- 
sible.^’ 

8.92. At the time there w.as a great 
need for samples of ’■elativelj' pure 
uniniura-235 for experimental pur- 
poses, and E. O. LawTence, of the 
Xhuversity of Califonnn, thought that 
tills could be most readily obtained by 


205 

the use of the electromagnetic sepa- 
ration procedure. Therefore, toward 
the end of 1941, he and his associates 
set out to improve the design of the 
apparatus, devoting particular atten- 
tion to methods for increasing the 
strength of the ion beam without im- 
pairing too seriously the efficiency of 
isotopic separation.* 

8.93. The W'ork proved so successful 
that, in spite of its apparent initial 
lack of promise, it was decided in 
September 1942 to build a large plant 
at Oak Ridge, Tennessee, consisting of 
a number of entirelj’^ independent units, 
for the electromagnetic separation of 
the isotopes of uranium. Subsequently, 
the yield of uranium-235 was con- 
siderably improved by using as feed 
material a compound of uranium which 
had been partly enriched in the 235 
isotope by the thermal diffusion method 
to be described below (§ 8.100). Since 
the positive-ion beam consists of the 
unwanted uranium-238, as w'ell as the 
wanted uranium-235, it is evident that 
for a given strength of the total ion 
current, the number of uranium-235 
ions, and hence the quantity of this 
isotope collected, wall increase as its 
abundance in the system is increased. 

8.94. The t^-pe of electromagnetic 
unit at present in use at Oak Ridge, for 
the separation of the isotopes of ele- 
ments other than uranium, is essen- 
tially equivalent to the Dempster mass 
spectrograph described in (§ 8.51).' A 
stream of electrons, emitt^ from an 
electrically heated wire, passes through 
the v.apor of a suitable volatile com- 
pound of the element whose isotopes 
are to be separated. A beam of posi- 
tively charged ions thus produced at 
the ion source A (Fig. 8.8) passes 
through slits in the plates PP; here 


cjvlifti R rahilrftn, a co-atractioii of “California Umver«itv cvclolron 
il tR!sd.- unc of t.).' magnet from ono of the University of California cyclofroii (§*9.67 



206 


Sourcdfook on Atomxc Energy 


they are accelerated by an electric 
potential V applied between these 
plates The ion beam then enter* a 
magnetic field of strength H, acting m 
a direction perpendicular to the plane 
of the diagram, so that it is bent 
through a semicircle The actual path 
of the positii el} charged particles de- 
pends on their masses, m accordance 
mth equation (8 7), i c , 

Tn ^ 

e 2V’ 


so that for a given electric and mag- 
netic field, the square of the radius of 



ffre path xs pruportionaf to the mass of 
the particle By placmg coUecting 
pockets m the proper positions, as 
calculated from this equation, the dif- 
ferent isotopes of a given element can 
be separated Althoiigli tn o such pock- 
ets are shown m the figure, three, foui 
or more can be used when necessary, so 
that several isotopes of the elements 
can be collected simultaneously 
8 95. In order that the same appa- 
ratus may be easily adaptable to the 


Chap VIII 
separation of light isotopes, such as 
those of lithium, mass numbers 6 and 
7, as well as of heavy isotopes, like 
those of lead, mass numbers 204, 206, 
207 and 208, the position^ of the 
ion source and the receivers are not 
changed, that is to say, the radii of the 
paths are kept approximately con- 
stant, but the magnetic field is altered 
as required Since by the equation 
given above, the mass m of the positive 
particles is proportional to i e , 
to the square of the magnetic field 
strength, for a given path radius, it 
follows that a six-fold increase m the 
field strength will permit a thirty-six- 
fold increase m the mass of the iso- 
topes that can be accommodated The 
fine adjustment that may be necessary 
to bring the ion beams exactly on to 
the receiver, with its properly spaced 
pockets, IS made by changing the ac- 
celerating volthge V In this manner, 
elements covering a large range of 
masses can be readily handled m any 
one electromagnetic unit It is ex- 
pected that relatively pure specmieas 
of some 180 different isotopes, of be- 
tween 40 and 50 elements, will be 
obtainable m amounts from a few 
milligrams to several grams * As re- 
cently as 1942, this accomplishment 
mthm the succeeding decade would 
have been regarded as highly improb- 
abfb 

The Centbifugal Method 
898. The gravitational force acting 
on a particle is proportional to its 
mass, consequently, under the influ- 
ence of gravity there is a partial sepa- 
ration of the gases of the atmosphere, 
tlie lighter molecules tending to stay 
in the upper levels while the heavier 
on^ concentrate in the lower levels 
This accounts for the fact that at great 


Such isot^es as are now available can be obtained, for approved research projects, from 
Ine Isotopes Division, 17 S Atomic Dncrgy Commission Oak Itidge, Tennessee 




Isotopes 


hoighls there is more hydrogen and 
helium, "which arc the lightest con- 
st ituenta of the atmosphere, than at 
the surface of the earth. The sug- 
gestion that this principle might be 
n]>plicd to the separation of isotopic 
molecules, ^Yith different masses, vfas 
made by F. A. Lindcmann and F. W. 
Aston in England in 1919. They 
showed that appreciable separation 
could be achieved by tiie use of a 
rentrifnge, for this would provide a 
force analogous to gravit^y, but much 
more powerful. The theor}- of the sub- 
ject WJI.S further examined in 1922 bj' 
B. S. Mullikcn, in the United States, 
who proposed an improved procedure 
which, making use of combined centrif- 
ugal force and evaporation, would give 
better results than the former alone. 

8.97. The basis of the centrifugal 
method of .separating isotopes is that 
if a ga-s or vapor flows into a rapidly 
rotating cylinder the force acting on 
the molecules will result in an in- 
creased concentration M the’- heavier 
isotope at the walls, while the lighter 
isotope tends to collect nearer the axis 
of rotation. If the centrifuge is verti- 
cal, a cuiTcnt of vapor can be made to 
flow dov\-n near the walls and up 
around the central axis; it should then 
be possible to draw ofl a product richer 
in the lighter isotopic species at the 
lop of the apparatus, near the center, 
while the hea\’icr species would be 
removed at the bottom near the pe- 
riplion*. 

8.98, A particularly intcrc-sting fea- 
ture of the centrifugal method i.s that 
the separation factor depends on the 
oitf'-ri'acr hctwcMt the ma.'sses of the 
lAvor-atopic elements!, and not on their 
ratio, llius. better separation .riiould 
Iwe obtainable, in principle, of the 235 
and isotopes of tu-anium thaw of 
the i^.aUipo^" of hydrogen, with ma.s: 5 cs 
Os 1 ana 2, rf‘-’j>ectiYely, Further, since 


207 

the difference in the isotopic weights is 
always the same for a given element, 
the efficiency is independent of the 
molecular weight of the compound 
whose vapor is being centrifuged. 

8.99. The earliest attempts to make 
nsc of this principle for the separation 
of isotopes failed, probably because the 
speeds of rotation of the centrifuges 
were not high enough. But in 1939, 
J. W. Beams, and others, in the United 
States, using the high-speed centrifuge, 
Avhich he had developed, and which 
produced a force of several hundred 
thousand times that of gravity, ob- 
tained appreciable separation of the 
isotopes of chlorine, in carbon tetra- 
chloride, and of bromine, in ethyl 
bromide. Since the atomic weights of 
the two isotopes of uranium differ by 
three units, the centrifugal method 
seemed to offer an especially attractive 
possibility for the separation of ura- 
nium-235. A pilot plant for this pur- 
pose was constructed during the war, 
and altliough it operated successfully, 
large-scale production by the centrif- 
ugal method was not attempted be- 
cause, as the Smyth Report says, "of 
the magnitude of the engineering prob- 
lems involved.” 

The THERxtALf-DiFFXJBioN Method 

8.100. Another plant for the sepa- 
ration of isotopes of uranium, which 
functioned for some time as a source of 
feed material for the electi’omagnetic 
plant, described in § 8.93, made use of 
the theimal-diffusion principle. The 
mathematical theory, which is appli- 
cable to any mixture of gases of differ- 
ent molecular v, -eights, was worked out 
between the years 1911 and 1919 by 
D. Enskog in Sweden and by S. Chap- 
man in England; later, in*^1922, the 
possible application to the separation 
of isotopes w'as examined by R, S. 
Mullikcn in the United States. 



208 


Sourcehooh on Atomic Energy Chxp Ylll 


8 101. The general idea is that if a 
gaseous mixture of isotopes is |:Jaced 
in a vessel, part of uhich is hotter than 
the remainder, the lighter molecules 
should tend to concentrate in the 
regions of higher temperature The 
experimental results were, at first, not 
very promising, but m 1038 the Ger- 
man scientists K ClusmsandG Dickel 
introduced a simple modification giv- 
ing a very decided increase m effi- 
ciency of the thermal-diffusion pro- 
cedure Their apparatus consisted of a 
long, Vertical tube with a central wire 
which could be heated electrically to 
about 500'*C or more, thus producing a 
temperature gradient between the hot 
wire and the colder wall of the tube 
The gas containing the isotopes to be 
separated is placed m the tube and, as 
a result of thermal diffusion, the lighter 
molecules collect near the hot wire, 
while the heavier ones prefer to stay 
nearer the cold wall At the same time, 
however, thermal convection causes 
the hotter gas in the center to nse while 
the colder gas at the wall sinks, so that 
there is a steady flow of gas, up at the 
center and down at the sides of the 
tube This continuous streaming of 
the gas, together with the influence of 
thermal diffusion, results m a concen- 
tration of the heavier isotopic species 
at the bottom of the tube,, while the 
lighter constituent tends to collect at 
the top In this manner, Clusius and 
Dickel were able to make rapid and 
effective separations of the isotopes of 
chlorine and neon Other workers, 
both m the United States and in 
Europe, applied the method to the 
elements ciwbon (m methane), nitro- 
gen, oi^gen, krypton and xenon 
8 102 Soon after the discovery of 
the combined thermal-diffusion and 
convection principles for separating 
gaseous isotopes, it was found that the 
method could be used for substances m 


solution and also for pure liquids In 
1940, T? H Abelson, in the United 
States, suggested applying the pro- 
cedure to liquid uramum hexafluoride 
for the purpose of separating the iso- 
topes of uranium After considerable 
experimental work had proved the 
feasibility of the method, a large-scale 
thermal-diffusion plant was built at 
Oak Ridge in the summer of 1944, its 
output, partially enriched in uranium- 
235, being used as feed material m 
the electromagnetic separation process 
“In spite of some disappointments,’ 
wrote H D Smyth, “operation of this 
plant succeeded m its purpose of 
considerably increasing the production 
rate of the electromagnetic plant " 
One of the principle drawbacks was 
Its great power consumption, and bo, 
when the gaseous diffusion procedure 
(§ 8 81) proved so efficient, and the 
electromagnetic separation became less 
important, the thermal-diffusion plant 
was closed down Nevertheless, for 
isotope enrichment on the laboratory 
scale, It appears that the thermal- 
diffusion method has advantages over 
others, because of its simplicity, e£B- 
ciency and wide applicability 

Distillation Methods 
8 103. Aston's first attempt to sepa- 
rate the isotojies of neon was made by 
fractional distillation, but, as stated 
in § 8 36, his efforts met with failure 
Subsequently, in 1919, F A Lmde- 
raonn, m England, showed theoreti- 
cally that separation of isotopes by 
distillation should be possible in cer- 
tain circumstances, and in 1931, W H 
K^om and H van Dijk, of Holland, 
reported the successful enrichment of 
the isotopes of neon in this manner 
In the same year, H C Urey and his 
collaborators used a form of distillation 
to concentrate the heavier isotope of 
hydrogen, as recorded in § 8 66 Slight 



Isotopes 


enrichment of oxygcn-18 and nilrogen- 
15 has been achieved by distillation of 
liquid oxygen and of liquid ammonia, 
respectively. 

8.104. In general, the separation of 
isotopic species by fractional distilla- 
tion is possible when their vapor pres- 
sures or boiling points are appreciably 
different. It was .stated in S8.71 that 
heavy water (D3O) boils at a temper- 
ature about 1.4°C higher than does 
ordin.ary water (H2O), This difference 
of boiling point, although small, should 
make separation by distillation practi- 
cal, provided an efficient fractionation 
column were used. Some success was 
reported in the United States by G. N. 
Ijcwis and H. E. Coniish in 1933, but 
the distillation method of separating 
the isotopes of hydrogen did not at- 
tract any great interest, because the 
relatively small amounts of hca\^ 
water or heavy hydrogen (deuterium) 
gjis required for e.xperimental purpo.scs 
could be obtained much more roadil}’^ 
by the electrolytic (§ 8.G9) or by the 
gaseous diffusion (§ 8.76) processes. 
During the war, however, it appeared 
pos.^ihle that large quantities of fairly 
pure heavy water might be needed 
in connection with the utiliz.ation of 
p.toinic energy* for military inirposes 
(§ M.2S), Since the elect I'oly tic process 
is C-xtnivagant in the use of electric 
power, con-sideration was given to the 
di.stiilat ion method of .sep.nrat ing the iso- 
topic forms of w.atcr. In .spite of the 
Inrfte steam consumption, a plant for 
tile pro'hu'rirm of heavy water by ex- 
tensive fractional distill.ation w.as built 
in 19*3. and operated in the following 
year. But it was later superseded by a 
more economical process, to be dc- 
serilHsi in § S.l 14, based on the isotopic 
exchange reaction referred to in § S.73, 

8.105. In addition to the isotopic 
(onus of hydrtigen, there .are present in 
Water, molecules which differ in the 


209 

oxygen isotopes; thus, about 0.2 per 
cent of ordinary water consists of H 2 O 
molecules containing oxygen-18. The 
boiling point of this isotopic species is 
slightlj’’ liigher than that of the pre- 
dominant form, with oxygen-16, and 
hence partial enrichment of the heavier 
isotopic form should be possible by 
fractional distillation. This expecta- 
tion was verified, in the years from 
1935 to 1937, by xvorkers in Canada, 
the United States and England; water 
containing up to five times the amount 
of oxygen-18 normally present, for ex- 
ample, was obtained by Urey and his 
coworkers. The product was some- 
what enriched in heavy hydrogen, but 
the actual percentage was quite small, 
probably of fhe order of 0.1 per cent. 

8.106. It is of interest to mention, 
in passing, that a form of distillation 
was used in 1920 by J. N. Brpnsted 
and G, Hevesy, in, Denmark, to achieve 
a slight enriclunent of the isotopes of 
mercurjg The liquid element, kept at 
about SO^C, was allowed to evaporate 
into an evacuated space, and the vapor 
condensed on a surface cooled in liquid 
air placed from 1 to 2 cm. above the 
mercury. The condensate was then 
allowed to melt, partially evaporated 
again, and condensed once more. After 
several fractionations of this kind, the 
lighter isotopes of mercurj' were found 
to be present in small excess in the 
condensate, while the heavier isotopes 
collected in the residue. In subsequent 
years a similar evaporation technique 
gave detectable separation of the iso- 
topes of the elements chlorine, zinc and 
potassium. 

The Electiiolytic Method 

8.107, It was recorded ia § 8,69 that 
electrolysis of aqueous solutions results 
in preferential evolution of the lighter 

I isotope of hydrogen, so that the dcutc- 
1 rium concentnates in the residual water. 



210 Sourcebook on 

The electrolyte generally employed is : 
potassium hydroxide, and almost any ^ 
electrodes, provided they do not dis- 
solve, can be used Nickel is a con- ' 
vement material for this purpose Sep- 
aration factors of 6 or higher are ' 
readily obtainable, so that concentra- i 
tion of the deutenum from its initial ' 
value of 0 02 per cent, in ordinary I 
water, up to 99 9 per cent in the prod- , 
uct, IS within the realm of possibility ! 
The current consumption is, however, 
very large, thirty or forty thousand 
ampere hours being required to yield 
one gram of heavy u ater It is for this 
reason that large-scale plants for the 
production of heavy water by the elec- 
trolytic method ^\ere erected in Nor- 
way, where electric power is relatively 
cheap Durmg the war these plants 
fell into enemy hands, and so became 
the object of several attacks from the 
air The purpose of these attacks was 
to interfere with experimental nork 
by German scientists on the develop- 
ment of atomic energy, in which heavy 
water could be used (| 14 28) 

8 108 Although in principle, the 
electrolytic method involves contmued 
decomposition of the water by the 
electric current until only a very small 
fraction of the original amount re- 
mains, this simple procedure would be 
very impractical For one thing, the 
dissolved electrolyte potassium hy- 
droxide, for example would become 
more and more concentrated as the 
electrolysis proceeded and for another, 
the hydrogen gas liberated toward the 
end would contain so much deutenum 
that it could not be wasted It is the 
practice, therefore to carry out the 
electrolysis m stages when the volume 
of water has been reduced to about 
one-tenth the residue is treated wth 
carbon dioxide to neutralize the potas- 
sium hydroxide and then the ennched 
water is distilled off The distillate 


Aimnxc Energy Chap VIIJ 

goes on to the next stage of electrolysis 
where the same procedure is repeated 
About five to seven stages are required 
to yield relatively pure heavy i\ater 
The hydrogen gas evolved in the later 
stages, and which contams a high pro- 
portion of deutenum, is burnt m oxy- 
gen to form water, this is condensed 
and returned to the electrolytic cells 

8 109 Durmg electrolysis hydrogen 
gite is given off at the negative elec 
trode (cathode), and oxygen gas at the 
positive electrode (anode) Just as 
there is a preferential e\ olution of the 
lifter isotope at the cathode, there 
should be a somewhat similar behavior 
at the anode leading to an enrichment 
of oxygen-18 m the residue The sepa- 
ration factor IS, however, little differ- 
ent from unity, and although the en 
nchment effect has been confirmed 
experimentally, it is \ ery small Elec- 
trolysis of lithium salts, using a mer 
cury cathode to collect the lithium 
metal, has also led to a partial sepa^ 
ration of the isotopes of this element 

Chemical Exchange Methods 

8 110 All the methods desenbed 
above for the separation of isotopes, 
with the possible exception of the elec- 
trolj'tic procedure, depend on differ- 
ences m physical properties determined 
by the masses of the isotopic species 
The discovery of the different reactiv- 
ities of the isotopes of hydrogen as 
desenbed in § 8 73, encouraged Urey 
and his students, between 1935 and 
1940, to investigate, both theoretically 
and expenmentally, the isotopic ex 
change reactions of other elements 
with a view to their use m the separa 
tion of isotopes Their efforts met wth 
remarkable success, and appreciable 
quantit es of compounds enriched m 
carbon-13 and nitrogen-15, respectively, 
were made m the laboratones of Co 
lumbia University before the ivork was 



Isotopes 


211 


takrn over by commercial organiza- 
tions.* 

8,111. Tiic method used with nitro- 
gen, for example, was to allow equi- I 
librium to be established between the 
14 and 15 isotopes of nitrogen in a 
system cou-sisting of ammonia (NHa) 
gas and ammonium ions. This 

was achieved by passing tlic gas up a 
column down which flowed a concen- 
trated solution of ammonium nitrate. 
As a result of the isotopic c.\'change 
reaction, the hcarw isotope (nitrogen- 
15) tends to concentrate in the ammo- 
nium ion in solution, while the ammonia 
ga-s contain.s relatively more of the un- 
wanted lighter isotope. Part of the 
ammonium nitrate solution withdraum 
at the bottom of the column is heated 
with sodium hydroxide, and this con- 
verts the ammonium ion into ammonia 
gas enriched in nitrogen-15. The re- 
sulting gas i.s then reproce.sscd udth the 
remaining portion of the ammonium 
nitrate solution, thus obtaining further 
enrichment. Urey and his coworkers 
used a ca.sc.adc system of three columns, 
operating on the countercurrent prin- 
ciple, the ammonium nitrate solution 
flowing downward and the ammonia 
gas upward. In this manner, they suc- 
ceeded in increasing the abundance of 
the nitrogen-15 isotope to more than 
TO ]>cr cent, as compared with the 
norninl 0.8S per cent, in spite of the rel- 
atively low separation factor of 1.023. 

8.112. .V similar procedure was used 
tvT concentrate carbon-13 from its usual 
proportion of 1.1 per cent to 22 per 
cent, by means of an isotopic exchange 
react inn between g;v«cous hydrogen cv- 
anide (TICX) and the cyanide (CN*) 
inn in s.^lium cyiinide solution. In this 


case, however, the hea\der carbon iso- 
tope concentrates in the gas phase, so 
that the desired product is withdrawn 
at the top of the column.f Some 
changes in the design of the apparatus 
are necessary but the principle is essen- 
tially the same as described for nitro- 
gen. 

8.113. As cyanides are poisonous, 
and consequently not too satisfactory 
for large-scale operation, an alternative 
process has been devised involving ex- 
change of the carbon isotopes between 
carbon dioxide (CO2) gas and the 
bicarbonate (HCO3") ion, in ammo- 
nium bicarbonate solution. The at- 
tainment of equilibrium is accelerated 
by means of a catalyst, and excess of 
the carbon-13 isotope is then found to 
be present in the bicarbonate solution. 

8.114. It was recorded in § 8.73 that 
in the isotopic exchange reaction be- 
tween hydrogen gas and liquid water, 
the proportion of deuterium in the 
water is about three times as great as 
it is in the gas phase, when equilibrium 
is attained. In other words, the hy- 
drogen-deuterium separation factor has 
the relatively liigh value of 3; conse- 
quently, appreciable enricliment of the 
heavj’- isotope should be possible by 
utilizing this reaction. One of the diffi- 
culties, however, is that the equilib- 
rium is established slowly, and hence a 
catalyst is neccssarj^ in order to ex- 
pedite the process. 

8.116. Since it was thought that 
large quantities of heavy water might 
be required for the wartime atomic 
energj’- project, a search was made for 
.suitable catalysts. This was succe-ssful, 
and a plant for the production of 
hc.avy w.ater by the method of isotopic 


protnh y areovint for thi^ rmaU TOrmlions in the Isotopic con 
f-’ clomcmi; «jch as cariwn and osj-gen, in nature; thus, atrao 

a vi- ""“IT from Lake Michige 

' 'V-f.; pr amt more than that from oce.an water. 

tv kotojHts, but this hf 



212 


Sourcehooh on 

exchange was erected in Bntish Co- 
lumbia, Canada, because of the availa- 
bility at this location of the necessary 
quantities of hydrogen gag The proc- 
ess IS superior to the electrolytic method 
m the respect that the power con- 
sumption IS low and also because it 
permits the use of standard engineer- 
ing practices The method used is to 
pass a mixture of hydrogen gas and 
steam upward through a tower con- 
taining the catalyst, while liquid water 
flows downward In, the presence of 
the catalyst, a rapid isotopic exchange 
reaction takes place between the hy- 
drogen and the water molecules in the 
steam, with the result that the deute- 
rium concentrates in the latter as 
deuterium oxide, that is, heavy water, 
molecules The steam is condensed, 
and hence earned downward by the 
flow of liquid water the water emerg- 
ing at the bottom of the toiler is thus 
considerably enriched m the heavier 
isotopic form By means of electrolysis 
the hydrogen gas with an increased 


Atomic Energy Chap Vlll 

proportion of deuterium, is liberated 
from the water and reprocessed Using 
a number of towers m cascade, in a 
manner similar to that already out- 
lined above, a product containing a 
large proportion of heavy water can be 
obtained at reasonable cost 
8 116 Other instances of isotopic 
enrichment by methods which utilize 
differences of reaction rates have beea 
reported But, it may be noted, that 
it IS only for the lighter elements that 
the procedure holds any promise at the 
present time As the atomic weight 
increases, the difference m the rates at 
which the isotopic species undergo ex- 
change reactions becomes very small 
and the separation factor is then very 
close to unity So far, 8uIfur-34 is the 
heaviest nuchde which has been con 
centrated by the isotopic exchange 
method, although there is little doubt 
that if it became necessary enrichment 
of even heavier isotopes could be 
achieved 



The Acceleration of Charged Particles 

Chapter IX 


NUCLEAR TRANSFORMATIONS 


Thk T'ransmutation of Elementc 

9.1. It was mentioned in Chapter I 
tiiat tile Aristotelian theorj’-, which re- 
gatxicd all matter as consisting of the 
Rsmo primordial substance associated 
with varying fsmounts of four qualities ; 
or principles, was probably responsible 
for the prolonged, but vain, efforts of 
the ancient alchemists to change base 
metals into gold. With the growth of 
the concepts of the individuality of the 
elements and of the indcstnictibility 
of the atom, particularly during the 
nineteenth centun.', it was natural that 
attempts to bring about the transmuta- 
tion of metals should full into dis- 
repute. Only those completely igno- 
rant of .science, and sufficiently gullible 
to bo, attnictcd by the possibility of 
tiio easy acquisition of riche.s, fell \'ic- 
tiin to the wiles of charlatans chaiming 
the ability to convert ba.se metals into 
gt^ld. 

9.2. With the development of mod- 
ern ideas concerning the .‘Structure of 
the atom, and the re.alirotion that all 
mrdter v.a,s made up of the .same funda- 
mental units, the possibility of trans- 
mutiit'.on, previously regarded as fan- 
tnsUo. wjiK given rerious consideration. 
In tact fcveml reports — some of them 
from scjcntssts of considerable repute 
j.t.jcces.s in changing or disintegrat- 


ing various elements were published in 
the scientific journals, both in Europe 
and in America. With the exception 
of the results to be described shortly, 
all were subsequently proved to be 
unfounded, but one is worthy of special 
mention because of its apparently con- 
\’incing nature. It was claimed that the 
passage of a high-tension electrical dis- 
charge through mercury vapor, atomic 
number 80, produced small amounts of 
gold, atomic number 79. The original 
mercury was apparently completely 
free of gold, yet the use of an extremely 
sensitive microscopic test showed the 
presence of traces of the precious metal, 
following the electrical treatment. After 
considerable controversy among the 
proponents and opponents of this plaus- 
ible claim, it was ultimately proved 
that the gold was not being created 
but merely concentrated from the vari- 
ous materials used. Much of it, in 
fact, came from the gold-framed eye- 
ghisses of one of the observ'ersl 

9.3. It was Rutherford, whose name 
has been frequently mentioned in these 
pages, who achieved the first deliber- 
ate, artificial transmutation of one atom 
into another. Although he did not 
convert a base metal into gold, his 
discovcty was just as important to 
nuclear science. 



214 jSource&ool. on 

TKANSJnJTATION OP NiOTOGEN 
BY Alpha Pabticles 
9.4. While working m Rutherford’s 
laboratory, m Manchester, England, 
on the scattering of alpha particles, as 
described in § 4 7 ci seg , E Marsden 
noted, m 1914, that when the radiar 
tions from radium C' passed through 
hydrogen gas, they produced a number 
of high-speed, long-range particles, ap- 
parently protons Some three years 
later Rutherford began a remvestiga- 
tion of Marsden’s work, in the course 
of which he studied the effect of alpha 
particles on several gases, m addition 
Co hydrogen The apparatus used was i 



Fio 9 1 Diagram of apparatus used by 
Rutherford to detect transmutation of 
nitrogen nuclei by alpha particles 

very simple (Fig 9 1) , it consisted of a 
metal cylinder m which was supported 
the radioactive source A of alpha parti- 
cles A small hole at one end was 
closed with a thin metal disk B capable 
of stopping most of these particles, 
and one or two miUimeters away was 
a zinc sulfide screen C Any long-range 
particles formed by the action of the 
alpha particles on the gas in the cylin- 
der were able to pass through the disk 
B and produce scintillations on the 
zinc sulfide (§ 6 40) Different gases 
could be admitted to the cylinder, and 
the effect of the alpha particles ob- 
served 

9 6 Reporting m 1919 on the results 
of his experiments, Rutherford wrote* 
“On introducing oxygen or carbon di- 
oxide into the vessel, the number of 
scintillations fell off in amount cor^ 
responding with the stopping power of 


Atomic Energy Chap IX 

the coliimn of gas An unexpected 
effect was, however, noticed on intro- 
duemg dried air . Instead of di- 
minishing, the number of [long-range] 
scintillations increased It was 

clear from these results that the alpha 
particles m their passage through air 
gave rise to long-range scintillations 
which appeared of about the same 
brightness as H-scintillations [i e , the 
long-range scintillations produced by 
alpha particles in hydrogen] ” 

9 6 Careful investigation showed 
that neither oxygen, carbon dioxide 
nor moisture was responsible for the 
beJiavior observed with air, but the 
effects could be closely duplicated with 
nitrogen gas m the cyhnder Conse- 
quently, the interaction of alpha parti- 
cles with nitrogen atoms or molecules 
results m the ejection of long-range, 
that IS, highly energetic, particles sim- 
ilar to those obtained ivith hydrogen 
“It is difficult to avoid the conclusion,” 
said Rutherford, "that these long-range 
atoms arising from the collision of al- 
pha particles with nitrogen are not 
nitrogen atoms but probably charged 
atoms of hydrogen If this be 

the case, we must conclude that the 
nitrogen atom is disintegrated under 
the intense forces de\ eloped in a close 
Collision with a swift alpha particle” 
9.7. Further work proved Ruther- 
ford's conclusions to be correct, and 
thus he achieved the first controlled 
artificial disintegration of an atomic 
nucleus The extent of the dismtegra- 
tion was, however, extremely small, 
for it was estimated that only one 
alpha particle m about 300,000 ex- 
pelled a long-range particle from tt 
nitrogen atom It is of interest to 
record that m his successful realiza- 
tion of nuclear transmutation, Ruther- 
ford was able to confirm a possibility 
which he had considered m his ’William 
Ellery Hale lectures, delivered m Wash- 




The Acceleralion of Charged Particles 215 

incton D. C., in April 1914. "It is possibly, beryllium, were found to emit 
possible " he sfiid, “that the nucleus protons when subjected to the action 
of an atom may be altered by direct of alpha particles. The energy of the 
collision of the nucleus with vety swift protons, as determined from their range, 
eleefrons or atoms of helium [i.e., al- was shown to be higher in some cases 
pha particlc.s] such as are ejected from than that of the impinging alpha parti- 
radionctivc matter. . . . Under favor- cle, thus indicating tliat they resulted 
.able conditions, these particles must fromadismtegrationprocep,theaddi- 
passver}' close to the nucleus and may tional energj'' being acquired in the 
either lend to a disruption of the nu- accompanjdng nuclear rearrangement, 
cleus or to a combination with it.” 9.9. At the time this work was being 

done, between the j’^ears 1920 and 1924, 
hlixiiAxisM OF THE Ntjceeau nature of the nuclear process which 

PiiocKSS led i;q the emission of protons was un- 

9.8. Following upon Rutherford’s pi- certain. Two possibilities were con- 
onecr cxqicrimcnts, he and Chadwick, sidcred: first, that the nucleus of the 



Fjg. 9.2. Blackett's photograph of alpha-particle cloud tracks in nitrogen. 
(From ‘'Radi.ntions from Badionctiyc Substances” by Rutherford, Ciiadwick 
and EHLh, Tlie Macmillan Comp.an}’, New York.) 


using an improved form of apparatus, 
m.nde a more detailed study of the 
action of alpha particles on various 
elements. By ob.-'Cn'ing the deflection 
of the result mg long-ninge particles 
in a mngtrelic field, Rutherford and 
Chadu ick proved t h.'it t hey were indeed 
paritively rh.arped hydrogem atom.s, or 
protons, of high rnerg>-. All the cle- 
nu'nts 5rom Imron to pota-^vrium, with 
the oxc, ption O! carbon, oxwgen and. 


disintegrated atom merely loses a pro- 
ton as a result of the severe impact 
accompanying collision with a fast- 
moving alpha particle; and, second, 
that the aljrha particle enters the nu- 
cleus of the atom which it strikes, the 
resulting combined nucleus then eject- 
ing a proton. The problem would have 
l)een solved if the nucleus remaining 
after emission of the proton could bo 
identified, hut there seemed no way in 




216 


Sourcebook on Aiomic Eriergy Chap IX 


which this could be done, particularly 
in view of the very small number of 
atoms actually undergoing dismtegra^ 
tion 

9 10 However, in 1925, P M S 
Blackett, in England, and in the fol* 
lowing year, W D Harkins, m the 
United States, independently obtained 
evidence which permitted of a decision 
between the two possible mechamsms 
indicated above From photographs of 
the tracks produced by alpha particles 
passing through nitrogen in a Wilson 
cloud chamber (§ 6 50), it could be con- 
cluded that the alpha particle disap- 
peared in the disintegrating colhsion, 
and so the second of the alternatives 
w as probably the correct one Blackett 
took over 20 000 photographs, depict- 
ing a total of more than 400 000 alpha- 
particle tracks, of these, eight were of 
the forked type, of w-hich an example 
IS shown in Fig 9 2, taken by two 
cameras at right angles to one another 
Each of these forked tracks undoubt- 
edly represents a collision between an 
alpha particle and a nitrogen nucleus 
leading to disintegration The long, 
thm track is that of the proton which 
IS ejected, while the short, heavy track 
IS due to the remaining (recoil) nucleus 
This appears, from the cloud track pho- 
tograph, to have undergone a colhsion 
which changed its direction It should 
he Rientioiied si&cs the artre^n 
atom, before bemg struck by an alpha 
particle, is neutral and has no ionizing 
power, its path cannot be observed in 
the cloud-chamber photograph The 
product, on the other hand, Carnes an 
electnc charge due to the loss of elec- 
trons in the collision, consequently it 
has the ability to produce ions m its 

Nitrogen Alpha 

Nucleus Partide 
14 4 

7 2 


path, and so forms a definite cloud 
track 

9 11 If the disintegration process 
had been the result merely of a dis- 
ruption leading to the expulsion of a 
proton from the nitrogen nucleus, there 
should have been a total of four tracks 
rather than the three actually observed 
In addition to the tracks of the proton 
and of the recoil nucleus, the path of 
the alpha particle should have been 
apparent before and after the collision 
Since the photographs do not show 
more than three tracks meeting at a 
point, it may be concluded that the 
alpha particle has entered the nucleus 
of the nitrogen atom with the forma 
tion of an unstable system, referred 
to as a compcAind nucleus, which im- 
mediately expels a proton 

Nuclear Rearranoebient 

9 12 Assummg the foregoing mech- 
anism to be correct, it is a simple 
matter to determine the nature of the 
recoil nucleus remaining after the pro- 
ton has been emitted The argument 
is based on the reasonable postulate 
that m the nuclear reaction there is no 
change m the total numbers of neutrons 
and protons, although the nucleons 
will be arranged differently before and 
after the collision The sum of the 
neutrons and protons is equal to the 
mass number, and the ntfnrter o! pw- 
tons is equal to the atomic number 
(§§ 4 36, 8 58 footnote) Both these 
numbers must, therefore, balance on 
the two sides of the equation rep- 
resenting the nuclear rearrangement 
Thus the interaction between an alpha 

particle and a nitrogen nucleus may 
be wntten as follows 

Compound Recoil 

— » Nucleus Proton + Nucleus 

(18) 1 17 

(9) 1 S 


Mass number 
Atomic number 



217 


The Acceleration of Charged Parlicks 


9.13. It Ss seen that the residual 
nucleus must have a maas of 17 units 
and an atomic number 8; this is the 
atomic number of oxj-gen, and so it 
follows that the product is an iso- 
tope of oxygen with a maas of 17 on 
the atomic weight scale. Indicating the 
various nuclei by the symbols of the 
corresponding elements, and inserting 
the maas number as a superscript and 
the atomic number as a subscript in 
each ease, the disintegration or, more 
eorreelly, the nuclear transformation 
or rearrangement, may be conveniently 
represented by the equation 

-b -> 

the maas nunrbers and the atomic num- 
bers, re.spectivcly, adding up to the 
sanvc amounts on the two sides of the 
equation.’^ 

9.14. Procc-ascs of this and related 
types arc freqticntly referred to as 
atomic (or nuclear) disintegration or, 
more colloquially, as “.atom smashing.” 
But it is in a few eases only that the 
nurleu.‘< is actually disintegrated, or 
sma-vhed, in the sense of being broken 
up into small fragment. As a general 
rule, nuclear reactions involve a simple 
nnirnangement of (lie protons and neu- 
trons among the nuclei concerned. It 
is preferable, therefore, to .speak of 
them either as luiclcar rearrangements 
or {IS jiuclcar tmnsformations or trans- 
mui.ations. They may be qualified as 
“artificial,’' to distinguish them from 
radioactive cbange.s which are spon- 
?,ine<n!s nuclear transmutations. 

9.15. Incidentally, it may be pointed 
out t hat , apart from the energj’ elianges 
in.volvc i, a miclear reaction and an 
ordin.ary chemicjil reaction ttre similar 
ns pritjciplc. In the latter, the process 

i>rco!npan!f‘<i by a re.’.rrnjigcment of 


the atoms, whereas in the former the 
nucleons, i.e., the protons and neu- 
trons, are rearranged. The change in 
the grouping of the nucleons associ- 
ated with the interaction of the nitro- 
gen nucleus and an alpha particle may 
be represented as follows: 

N -f He -> H + 0 

Protons 7 2 18 

Neutrons 7 2 0 9 

and it might even be written as: 

p^n^ -b pin^ — » p -b Psth, 

where p and n represent a proton and 
a neutron, respectivel 3 ^ 

9.16. Although it is convenient to 
record for each participating nucleus 
both the symbol and the atomic num- 
ber, this is really unnecessary since one 
includes the other; thus, the sjunbol N 
(for nitrogen) can refer onlj’- to the 
element of atomic number 7, and vice 
versa. On the other hand, the mass 
number must always be noted, for 
othen\*ise it would not be known which 
particular isotopic form is involved. 
Utilizing these facts, a verj’- simple 
scheme, now widely used, w'as devised 
in 1935 bj' W. Bothe in Germany for 
describing nuclear processes. The re- 
action under con.sideration, for exam- 
ple, can be formulated as N'T«,p)0‘^, 
which would be interpreted as follows: 
a nitrogen (N*^) nucleus interacts ndth, 
j and engulfs, an alpha (a) particle, a 
proton ip) i.s ejected and a nucleus of 
an oxygen (0") isotope remains. The 
general group of nuclear reactions stud- 
ied by Rutherford and Chadwek can 
then be referred to as being of the 
(a.p) t^qie; in these processes, the al- 
pha particle is the incident particle, 
while a proton is e.xi)elled. 


■!'?' *V' ppbek' has ixa:n repres-entod in the equation as a helium 
^ AlUx \ i.rii U of identical. 



218 SouTcd>ooh on 

Bosibabdment of Atomic Nuclei , 
BY Charged Particles 

9 17 By 1924, Rutherford and Chad- 
wick had established that nearly all ' 
the lighter elements up to and includ- 
ing ^potassium emitted protons when 
subjected to the action of alpha parti- 
cles But with heavier atoms there 
was only scattering of these particles 
(§ 4 7) indicating that they did not 
have sufficient enei^y to penetrate the 
atomic nucleus In receiving the prog- 
ress made during the years 1925 and 
1926, on “the disintegration of nuclei 
by the impact of alpha rays," F W 
iGton (see § 8 36) ivrote “']^ere has 
now come the inevitable period of 
quiescence awaiting the development 
of new weapons “ Actually, some six 
years were to elapse before new raeth- i 
ods of attacking the atom became j 
available, ivith consequences that could j 
certainly not have been foreseen I 

9 18 It was shown m § 4 16 that, | 
at any distance d, the energy of repul- | 
Sion of aa alpha particle, carrying two j 
unit positive charges, by an atomic [ 
nucleus, with Z such charges — Z being | 
equal to the atomic number — is 2Z€'*/d, \ 
where e is the unit (electronic) charge 
It is thus evident that the energy with 
which an alpha particle is repelled from 
a nucleus increases with the atomic 
number Consequently, particles which 
niigftd fte siiSScieatly energetic to ap- ' 
proach the nucleus of a light element 
would be turned back by a heavier 
nucleus, with hi^er atomic number 
It was thus apparent to Rutherford, 
and others, in the late 1920s, that 
progress in the study of nuclear dis- 
integration required the construction 
of devices which would provide parti- 
cles ivith greater energy than the alpha 
particles obtainable from natural radio- 
active sources 

9 19 According to classical electro- 
static theory the energy which an al- 


AUmtc Energy Chap IX 

pha particle would require in order to 
reach the nucleus of an atom, that is 
to say, to be able to surmount the so- 
called potential bamer (§ 7 28), for 
elements of higher atomic number, 
would be from 20 to 30 Mev In 1930, 
such high energies, although now fairly 
commonplace, were quite out of reach 
It was fortunate, therefore, that at 
about the same time, the application 
of wave mechanics to the problem of 
nuclear penetration, as explamed m 
Chapter VII, showed that particles 
would both leave and enter the atomic 
nucleus ev en though their energy was 
considerably less than that of the top 
of the hypothetical bamer 
9 20 The first experiments on nu 
clear transmutation were naturally ear- 
ned out nith Bvnit alpha particles be- 
cause of their availability, but the 
wave-mechamcal calculations made by 
G Gamow in 1928 suggested that other 
charged particles might be more effec- 
tive He showed that not only was the 
energy barrier lower, but the probabil- 
ity of penetratmg it and reaching an 
atomic nucleus also increased, as the 
charge and mass of the mcident particle 
decreased Thus, for a given value of 
the particle energy, a proton, with umt 
charge and unit mass, was much more 
likely to enter the nucleus than an 
alpha particle, carrying two charges 
s cJ SioiJT muts- In 
fact, it appeared that m order to at- 
tain a particular probability of reach- 
ing a given atomic nucleus, an alpha 
particle would need to have something 
like sixteen tunes the energy of a pro- 
ton A small number of fast-movuig 
protons are, of course, ejected in the 
(o,p) type of process discovered by 
Rutherford, but the number is so in- 
significant as to be useless for practical 
purposes Consequently, interest was 
aroused in many scientific laboratories 
m the possibility of developing meth- 



219 


The Acceleration of Charged Particles 


ods for building up high potentials, 
of the order of hundreds of thousands, 
or even millions, of volts, vherebj' 
protons, i.e., charged hydrogen atoms, 
could be given sufficient energy to pen- 
etrate atomic nuclei. 

Distintkghation of Lixinrai 
BY Protons 

9.21. Tlie more important of the de- 
vice.*? by mcims of which high-energj'’ 
particles can be obtained will be de- 
scribed below. In the meantime it 
may be stated that the first successful 
])roduction of protons with sufficient 
energy to cause nuclear transforma- 
tion was achieved in Rutherford’s lab- 
oratory in Cambridge, England, by 
.1, D. bockcroft and E. T. S. Walton 
iti 1932, Their work stands out in 
the history of nuclear science as be- 
ing the first case of nuclear disinte- 
gration brought about by purely artifi- 
cial means. Rutherford had used swift 
alpha particlc.s from natural sources, 
hut in the experiments of Cockcroft 
and Walton protons, obtained by the 
ionization of hydrogen in a discharge 
tube, were accelerated by means of 
high volUnges. R'lien the light element 
lithium, in the fonn of a layer of lith- 
ium o.vide, was bombarded by fast- 
moving protons, bright scintillations, 
due to particle.s ejected from the lith- 
ium, wore immediately observed on a 
rim; sulfide screen placed a short dis- 
tance aw.ay, Tlio scintillations were 
fjnt detected wliem the accelerating 
potenti.'il uas about 125,000 volts, the 
mtmhcr incrc.asing with increasing volt- 
ago. At 250.000 volts there was one 
scintillation for about a billion protons, 
and at double this voltage the number 
wo incrcoetl ten-fold. 

9,22. Subsequently, Cockcroft and 
V« alt on made ob^-erwations of the t racks 
of thoejfctcd partioles in a cloud ebam- 
K’r, and they reported that "the bright- 


ness of the scintillations and the den- 
sity of the tracks suggest that the 
particles are normal alpha particles. 
... It [therefore] seems not unlikely 
that the lithium isotope of mass 7 
occasionally captures a proton and the 
resulting nucleus of mass 8 breaks into 
two alpha particles of mass 4.” The 
nuclear reaction thus achieved may be 
WTittoD as 

-f "He' + iHeS 

the proton being indicated by the sym- 
bol iH* and the alpha particle by sHe^. 
Utilizing the abbreviated method of 
formulation described above, the proc- 
ess would be represented as Li^(p,a)He^, 
although there is actuallj^ no differ- 
ence between the alpha particle, rep- 
resented by a, and the helium nucleus, 
indicated by Heb It is , particularly 
significant that, in agreement with the 
calculations of wave mechanics, the 
process occurred to a detectable extent 
Avith protons of about 125,000 ev, i.e., 
0.125 Mev, a value considerably less 
than the height of the potential barrier 
between a litluum nucleus and a proton. 

9.23. Support for the postulated dis- 
integration was obtained from several 
different directions. Cloud-chamber 
photographs, made by P. I. Dee and 

E. T. S. Walton in England and by 

F, ICirchner in Germany in 1933, 
showed two tracks of equal length, 
mddently due to alpha particles, emerg- 
ing in opposite ditections from a lith- 
ium target bombarded by the high- 
energj’ protons. If the miclear process 
resulted in the formation of two alpha 
particles, as postulated above, then 
they would, in fact, be expelled in op- 
posite directions in order to comply 
A\-ith the requirement of conservation 
of momentum. 

9.24. Proof of the supposition that 
it is the more abundant litluum iso- 



220 Sourcebook on 

tope, mass number 7, that is involved 
m the production of alpha partides 
was provided in 1934 bj Rutherford’s 
students M L K Ohphant, E S 
Shire and B M Crouther Fairly 
pure specimens, a few millionths of a 
gram m weight, of the Li® and Li^ 
isotopes of lithium vere collected on 
small targets, using the electromag- 
netic separation procedure (§ 8 89), and 
bombarded mth accelerated protons 
The results showed definitely that the 
Li^ isotope gave two alpha particles, 
the Li® isotope also exhibited a nuclear 
reaction, but it was of a different type, 
as might be expected 

Nucleap, Reaction Energies 
9 26 Nuclear reactions, involving a 
rearrangement of the nucleons, resem- 
ble ordinary chemical reactions, m 
which there is a redistribution of whole 
atoms, in the respect that they are ac- 
compamed by energy changes The 
nuclear energy changes are, however, 
usually very much larger, they are of 
the order of millions of electron volts, 
as compared with one or two electron 
volts for most chemical reactions The 
over-all energy liberated or taken up 
m a nuclear process is called the nuclear 
reacitan energy^ and is generally repre- 
sented by the symbol Q, for this reason 
the energy change is sometimes referred 
to, in bnef, as the “Q” of the nuclear 
reaction The value of Q may be posi- 
tive or negative depending on the na- 
ture of the process 
9 26 According to the Einstein the- 
ory of the equivalence of mass a^d 
energy, the nuclear reaction energy 
must be exactl}' balanced by the changes 
in mass associated with the reaction 
Thus, if Q is positive, that is to say, 
if the process is accompanied by the 
liberation of energjq there must be a 
decrease of raa'?s, the total mass of 
the products will then be less than 


Aiomui Energy Chap IX 

that of the interacting nuclei by an 
amount equivalent to this energy On 
the other hand, a negative value of Q 
means that energy is taken up and 
there is a gain of mass m the nuclear 
reaction, such a result implies that 
the total mass of the products exceeds 
that of the onginal particles 

9 27. In the course of their work, 
Cockcroft and Walton made a com- 
parison between the changes of mass 
accompanying the interaction of lith 
ium-7 and a proton to form two alpha 
particles, and the energy liberated m 
the nuclear reaction, assuming the ap- 
plicability of the Einstein mass energy 
relations^p (§ 3 71) to such reactions 
They showed that the agreement was 
consistent with their mterpretation of 
the mechanism of the process, as given 
abo\e But there was no clear evi- 
dence, at the time, of the validity 
of the Einstein equation, and conse- 
quently, in 1933, K T Bambndge, in 
the United States, used the energy 
data, together with the known iso- 
topic w eights of lithium, hydrogen and 
helium, to pro\ ide a quantitative verifi- 
cation of the mass energy relation- 
ehip 

9 28 In the reaction between pro- 
tons and the lithium isotope of mass 
number 7, the nuclear energy liberated 
can be determmed by measunng the 
range, and hence estimating the en- 
ergy, of the alpha particles produced 
Cockcroft and Walton found this range 
to be approximately 8 cm m air, so 
that each alpha particle earned off 
about 8 5 J lev, making a total of nearly 
17 Mev for the nuclear reaction energy 
Later, more precise measurements of 
the alpha particle ranges showed that 
Q for the reaction was 17 2 Mev, after 
allow mg for the energy of the incident 
pioton, the energy of the bombarded 
lithium nucleus, which is a fraction of 
an electron v olt, is quite negligible in 



221 


The Accckralion oj Charged Particles 


coinpnrison with the other quantities 
i involved. 

9.29. The mass equivalent of 17.2 
Iticv can be readily derived by means 
of the Kinstein equation in the form of 
equation (3.22) which here becomes 

17.2 Mev = m (at. wt.) X 931, 

so that the mass equivalent on the 
atomic weight scale is found to be 
0.0185, Since there i.s a liberation of 
encrg>', that is to say, Q is positive, 
it may be concluded that in the nuclear 
reaction 

LP + H» -» He‘ + He' 


the sum of the masses of the products 
will be lo.ss than that of the interacting 
nuclei by 0.0185 atomic weight unit. 

9.30. In an equation of this kind 
it is the miissos of the respective nuclei 
which arc implied, but the same final 
result i.s obtained bj* using the atomic 
or i.'-'otopic weights which include the 
masses of the electrons. The number 
of elect ron-s i.s the same on both sides 
<if the equation, and so when comput- 
ing the loss or gain of mass in a nuclear 
reaction, the mas.'^cs of the electrons, 
if they arc included, will cancel.* The 
i-otopic weights of Li*. H* and He' are 
now known with con.siderablo accuracy 
from m5is.s-s})octrograi)hie determina- 
tioTS'^, so that the change of mass may 
he I'omjnited as follows; 


I fit trading 
Poriidcs 

1m 7.0 IS2 
IT l.OOSl 


Product 

Parliclrs 

He' 4.0039 
He' 4.0039 


S.0078 

DtfTcrcnrc' 

--- 8.0078 - 8.0203 -O.OlSo. 


9.31. The nuclear reaction under dis- 
cussion is therefore accompanied a 
loss of 0.01S5 unit of mass, on the 
atomic weight scale, and this is seen 
to be exactly equal to the mass equiv- 

I alent of the energy liberated, as esti- 
mated from the energ}*^ of the alpha 
particles. 

9.32. The identity of the figures in 
tliis case is partly fortuitous, but the 
fact that they are in agreement is a 
strong argument, as Bainbridge showed, 
for the applicability of the Einstein 
mass-encrg\' relationship to nuclear re- 
actions. This particular case is of spe- 
cial interest, not only because it was 
the first nuclear process bi’ought about 
by artificially accelerated particles, but 
also because it provided one of the 
earliest, if not the earliest, verifications 
of the Einstein equation. Since 1932 
numerousnuoleartransformationshave 
been studied in detail, and in every 
case for which sufficient data are avail- 
able, the value of the nuclear reaction 
energjq as calculated from the meas- 
ured energies of the incident and prod- 
uct particles, i,s exactly equivalent, 
udthin the limits of the experimental 
errors, to the change of mass accom- 
panying the process. There can thus 
be no question as to the validity of the 
Einstein equation in these cases or of 
the reality of nuclear transformations. 

DEXmMIXATION OF IsOTOPIC WEIGHTS 

9.33. An interc-sting consequence of 
the stud}' of the mass and energy 
changes involved in nuclear processes 
was the sugee-stion, made independ- 

I ently in 1935 by H. A. Bethe and by 
j aI. L. E. Oliphant, A. R. Kempton 
and E. Rutherford, that the mass- 
I spectrograpliic isotopic weiglits of the 
j lighter elf'inonts in use at that time 
j required correction. These investigat- 


trvr-itivc cl'»ctrtjn?} nro liberated 
5,' . ri'iiiox'e'' an elrcsron. 


arc exceptional in this ro- 



222 


Sourcf^ok on 

ors found that in certain nuclear reac- 
tions the energy change differed from 
the equivalent of the mass change by 
amounts exceeding the probable ex- 
perimental errors It was felt that the 
source of the discrepancies w as not m 
the mass spectrograph itself, but rather 
in the accepted isotopic n eight of 
helium, mass number 4, uhich was 
used as a comparison standard for the 
lighter elements The isotopic weights 
were consequently recalculated on the 
basis of an empirical correction m the 
helium value, and the results so ob- 
tained gave excellent agreement with 
the mass-energy prmciple A more 
careful companson by F W Aston 
of the isotopic weight of helium wnth 
that of oxygen, made m 1936, com- 
pletely substantiated this correction, 
and thus provided stnking evidence 
for the equivalence of mass and energy, 
at least m the nuclear processes 
9 34 It IS of interest m this con- 
nection to mention that the isotopic 
weights of certain nuclides which are 
either too unstable or too rare to 
be measured by mass-spectrographic 
methods are actually determined from 
nuclear reaction energies A case m 
point IS that of the oxygen isotope 0*^ 
which, as mentioned in § 9 12, results 


Atomic Energy Chay 

from the interaction of an alpha parti 
clc with a nitrogen nucleus, this reac 
tion, including the energy Q, may be 
written as 

+ He^ Hi -{- 0'’’ 4- Q • 

From the known energy of the alpha 
particle and the measured range of 
the proton, the nuclear reaction en 
ergy Q is found to be —1 16 Mev, the 
mass equivalent on the atomic weight 
scale, obtained upon dividing by 931, 
as seen above, is then —0 00124 
9 36 It w ill be noted that since Q 
has a negative value in this case the 
total mass of the products will be 
greater than that of the interacting 
particles The isotopic weights of N” 
and He* are 14 00761 and 4 00390 
respectively, making a total of 18 01141 
os the left-hand side of the equation 
On the right-hand side there is 1 00812 
for H* and —0 00124 fot the mass 
equivalent of 0, i e , 1 00688, in addi- 
tion to the isotopic weight of 0”, the 
latter is consequently given by 

0” = 18 01141 - 1 00688 =• 17 0045, 

the final significant figure being neg- 
lected 


PARTICLE ACCELERATORS 


The Voltage Multiplier 
9 36 Although it was not the first 
device for produemg charged particles 
of high energy, the voltage multiplier 
system employed by Cockcroft and 
Walton (§ 9 20) is important histon- 
cally because it w as the first with which 
artificial nuclear transformation was 


achieved The principle had previously 
been used for accelerating electrons, 
and in 1929 it was adapted by Cock- 
croft and Walton for use with protons 
which were thus obtained with en- 
ergies up to 380,000 ev However, it 
was not until two years later that the 
disintegration of the lithium nucleus 


* It is the usual practice to write these equations in the algebraic form with -|-Q, although 
the actual value of Q may be positive or negative Since in the case under consideration Q is 
— 1 16 Mev, the equation becomes 


N» + He« H‘ + 0« -1 16 Mev 


223 


The Acceleration of Charged Particles 


\iv protons with less than half this 
onergv rvns definitely recognized. _ 

9.37. The procedure may be illus- 
i rated by reference to Fig. 9.3. A 
iniinber of condenser.^ Ci, C;, Cs, Ga, 
etc., of cciual e.ap.'icity, are arranged as 
shown, together with switching mcch- 
iinisms Si, S 7 , etc.; the tran.sformer T 
is the source of a high-voltage altematr- 
ing potential. The switches Si, S 2 , 
etc,, arc actually vacuum tubes, and 


charge on Ci is transferred to C;, but 
in the next half cycle, Ci receives more 
charge which it again shares with C 2 
in the following half cycle. Eventually, 
both Cl and C 2 are charged up to the 
potential Vi, so that F 2 (Fig- 9-3, II) 
is twice Fi. The arrangement of two 
condensers Ci and C 2 , and’ two vacuum 
tubes Si and S-, acting as switches, 
is thus a voltage douhlef, and several 
such doublers in cascade constitute a 



Fio. 9.3. Princijilc of the voltage multiplier used by Cockcroft 

and Walton. 


ojK-rate in such a manner that when 
the alternations in T arc in one direc- 
tion, the switch »Si is closed while Sz 
is open (Fig. 9.3, 1); in the nc.xt half 
cycle, (he altcnmtion.s are reversed and 
Si is ojien while Sz is closed (Fig. 
9.3, II), and so on in successive half 
cycles. When Sj is closed, the con- 
densvr Ci i.v chargtxi up to the potential 
1 j (Fig. 9,3, 1), which i.s virtu.nlly that 
."'.ippficd hy the transfomier T. Upon 
ojH'ning Si ant! clo'-ing S;. part of the 


voltage nniltiplicr.* In one stage tlie 
voltage is doubled, in two stages it is 
quaduipled, in three stages it is in- 
crea.sed six-fold, and so on. 

9.38. Starting with a potential of 
about 100,000 volts across the sec- 
ondaiy coil of the transfonner T, Cock- 
croft and Walton were able to obtain 
an output of nearly 800,000 volts. This 
high potenti.-il was then used to accel- 
erate protons obtained by passing an 
clectnc discharge through hydrogen 


. utftiv •■s-as.ing, whtil hzi,> l». i-n i.iUwl lu-re, for .Mmphcitv, the .wUcIiing action of the 
inns 0!5 v„- ,S. vt rt-ally dieir .alnlity to act as vnlvi*«, which permit current to press 

Incv thu'^ act as rectifiers of the aitcrnatinK potential supplied bv the 
. .'rji,.r. iotnH:qufraly, the voltage multiplier is sometimes referred to os a cdxcatic 



224 


Sonrcchot^ on Atomic Energy 


gas In later forms of the apparatus, 
based on the voltage multipbcation 
principle, particle energies up to 3 Mev 
have been obtained The Cockcroftr 
Walton device has the advanta^ of 
simplicity, with no moving parts The 
maximum energies obtainable are low 
compared with those from other ac- 
celerators, described below, but it pro- 
vides fairly large ion currents at con- 
stant voltage, and hence it is very 
useful for experimental work requiring 
moderate potentials The voltage mul- 
tiplier can be used to accelerate other 
charged particles, such as alpha parti- 
cles (helium nuclei), deuteroos (deu- 
terium nuclei), and others, produced 
by ionization of the corresponding gas 

The Electrostatic Generator 

9 39 The essential principle of the 
high voltage electrostatic generator, de- 
veloped by R J Van de Graaff in the 
United States, is similar to that em- 
ployed in various forms of apparatus, 
such as the Wimshurst machine, which 
have been used in laboratories for many 
years to obtain discharges of static 
electricity The instrument makes use 
of two facts long familiar to physicists 
The first is that a conducting sphere, 
or other hollow body, is able to accept 
any available charge, irrespective of 
ite own voltage It is thus possible 
to build up the potential by continu- 
ously supplying electnc charge to the 
sphere The second fact is that dis- 
charge of electricity occurs readily at 
pointed objects 

9 40 The apparatus consists of a 
belt A made of paper, silk, rayon or 
other flexible, nonconducting matenal, 
which is run, by means of a motor, at 
high speed over two pulleys, as indi- 
cated in Fig 9 4 A direct current po- 
tential of from 5000 to 20,000 volts 


Chap IX 

IS applied at B, the positive pole being 
connected to a pointed comb-hke coa 
ductor, and the negative to a rounded 
body, one on each side of the moving 
belt, as shown at C As the moving 
belt passes by C, it picks up positive 
electncity* from the points, and con- 
veys it upward toward the large metal 
sphere D, sometimes called the corem 



Fia 9 4 Diagrammatic representation of 
the Van de Gra^ electrostatic generator 

cop, mounted on insulatmg supports 
At ^ a set of points connected to the 
sphere draw off the charge from the 
belt and transfer it to the sphere, thus 
building up an electneal potential on 
the latter 

9 41 In the later forms of the 
Van de Graaff electrostatic generator, 
a pointed conductor F, also connected 
to the sphere, is placed opposite the 


* Actually negatively charged electrons pass from the belt to the points thus leaving 
belt V. ith a positive charge 


225 


The Accchralion of Charged Particles 


rounded end of E. A discharge of 
negative electricity thus takes place 
from F, so that electrons are collected 
by and carried downward by the belt; 
tlic>c arc eventually removed at C and 
pass to the source B. This additional 
device docs not appreciably affect the 
maximum potential attainable, but it 
does increase the magnitude of the 
charged-particle current which the ap- 
paratus can supply. 

9.42. A.S the generator ojicrates, the 
voltage of the corona cap, with re.spect 
to the ciirlh, steadily increases until 
it reaches a jmint where the electric 
charge leaks away a.s fa.st as it is col- 
lected from the mo^dng belt. The leak- 
age can be minimized, and the maxi- 
mmn attainable voltage thereby in- 
creased, by enclosing the apparatus in 
a gas-tight steel chamber and operat- 
ing tmdor prc.ssure.s up to about 15 at- 
ino.sphores. The gas in the chamber 
may be air or nitrogen alone or, bet- 
ter, methane, difiuorodichloromethane 
(“Freon”) or sulfur hexafluoride mixed 
with air or nitrogen. 

9.43. In the first electrostatic gen- 
erator constructed by Van dc Graaff 
in 1031, the maximum potential at- 
tained was 1.5 million volt.s. In later 
forra.s thi.s was increased in stages up 
to a value of about 5 million volts. 
During 1918 preliminarj' work was 
started on two electrostatic generators 
capable of reaching potentials of 12 
million volts, with the possibilitj' of 
contimio\is variation dovm to quite 
small values by changing the voltage 
suppliefl at B (Fig. 9.4). Like other 
lorjns of the Van dc Graaff apparatus, 
tl'.f new acccleratons will give a good 
supply of rh.arged particles at volt- 

vhtch can be maintained con- 
‘ fruit within about 0.1 per cent. These 
rlfclrO'iatic generators will provide ac- 


curate quantitative data on the prop- 
erties of atomic nuclei. In addition, 
the verj' narrow, well-defined beams 
of energetic protons of definitely known 
energj’’ which will be a\milable should 
be of great value for the investigation 
of proton-proton and proton-neutron 
scattering; such studies are of funda- 
mental significance in connection with 
tire theory of nuclear forces (§ 12.75 
cl scq.). 

9.44. In both the voltage multiplier 
and electrostatic generator methods of 
producing lugh potenti.als means must 
be devised for the application of these 
potentials to the particular ions, or 
electrons, being employed. For this 
purpose special accelerating tubes have 
been designed; they are usually made 
up of sections of glass, porcelain or 
other insulating material joined end to 
end by vacuum-tight seals. The com- 
plete tube has to be long enough to 
eliminate the possibility of a spark or 
other discharge passing from one end 
to the other when the potential is 
applied. The high potential region of 
the A'ollage multiplier or electrostatic 
generator is connected to a hollow, 
cylindrical electrode at one end of the 
tube, while a similar electrode at the 
other end is connected to earth. Ions 
I are then sent through the accelerating 
! tube from a suitable source at the 
high-potential end to the target at the 
other end, acquiring increa.sing energj’- 
as they travel the length of the tube. 

The Likeak Accei.eratok 

9.46. An instrument, known as a 
linear accelerator, for producing posi- 
tive ion.s of highenergv' was const meted 
by D. II. Sloan and E. 0. Lawrence 
in the United States in 1931, utilizing 
n principle previously employed by 
R. Widerde in Genuany in 1929. Bo- 


* i'tfn at eSh' Al) 


Sf-k-atsfir I.ahoraton- and ilie other at the Institute 



226 


Smrcebook on 

cause of certain limitations of the appa- 
ratus, which will be indicated shortly, 
it was used only for the acceleration 
of heavy ions, and these were of no 
value for the study of nuclear trans- 
formation since they could not pene- 
trate atomic nuclei However, in recent 
years new devices have become avail- I 
able which make it possible to use the | 
same general idea for producing pro- 
tons of high energy It is woith while, 
therefore, to consider the linear ac- 
celerator, especially as it was the fore- 
runner of an instrument, to be described 
m the next section, which has played I 
a highly significant role m the progress 
of nuclear science 


Atomic Energy Cha^p IX 

947. Suppose positive ions from tbe 

source S move from left to right along 
the common axis of the cylinders. 
While passing through the first (or 
any other) cylinder, they receive no 
acceleration, since this has a uniform 
charge,* but m traversing the gap be- 
tween the first and second cylinders 
the ions are m a region in which there 
IS a difference of potential, if the first 
cylinder is positive and the second is 
negative, the positively charged parti 
cl^ vnW be accelerated in the gap 
The jonic particles then enter the sec 
ond cylinder and travel through it at 
a speed which is constant but higher 
than the initial value The length of 



Fir 9 5 Linear accelerator for positively charged 
jMirticles 


946 In essence, the linear acceler- 
ator consists of a number of cylinders, 
of increasing length, arranged m a j 
straight line, as represented m Fig 9 6 
Alteitiate cylinders are connected to- I 
gethpr, the first, third, fifth, etc , being 
joined to one terminal C-d) and the i 
second, fourth, sixth, etc , to another 
temimal (B) of a generator of high- I 
frequency electrical oscillations Atany 
instant, therefore, alternate cylinders I 
carry opposite electncal potentials, for 
example, m a particular half cycle of ' 
the oscillations, all the odd numbered 
cylinders ivill be positive while those 
ivith even numbers wiU be negative 
In the next half cycle the potentials 
ivill be reversed, so that the odd num- 
bers become negative and the even 
numbers positive 

* It is for this reason that the cylinders are 


this cylinder is such that just as the 
ions reach the gap between it and the 
third cylinder the potentials are re- 
versed The second cylinder is now 
positive while the third is negative, so 
that m passing through the gap the 
ions receive an additional impulse which 
accelerates them still further By mak 
lOg the successive cylinders increas 
mgly longer, to allow for the increasing 
speeds of the positive ions, it is possible 
for the ions to be kept exactly in 
phase with the alternations of poten 
ti^ Thus, whenever the ions reach 
a gap between two cylinders, the one 
on the left has a positive potential 
while that on the right is negative 
and so the ions acquire additional en 
ergy every time they pass from one 
cylinder to the next 
referred to as drift tubes or shielding h bes 



The Acceleration of Charged Particles 


9.48. li y volts is the potential pro- 
djiccd by the oscillator at the terminals 
A and B, the total energj' in electron 
volts acquired by a single charged ion, 
such as a proton, vdll be approximately 
equal to V multiplied by the number 
of gaps traversed. In this Vt&y Sloan 
and Lawrence, u.singan apparatus wth 
some thirty cylinders, v'ere able to 
obtain mercury ions of 1.20 Mev en- 
ergy, .although the source of potential 
was only 42,000 volts. Sub.scqucntly, 
an energy of 2.85 IMcv was obtained by 
raising the oscillator potential to 79,000 
volts and using additional cylinders to 
inerca.se the number of gaps. 

9.49, Because the oscillation fre- 
quency of the high-frequency oscil- 
latnns available in the early 1930s was 
not- really high enough, it was neces- 
sary to work with relatively heavy, 
sUnv-nioving ions, such as those of 
mercury. If the lighter ions, of hydro- 
gen (prolon.s) or helium (alpha parti- 
clc.s), for example, had been used, the 
cylinders would have had to be made 
iiK cinvcriicntly long so ns to allow suf- 
fick-nt time for the potential to be 
reversed while the fast-moving ions 
wetf jiassing through them. The ad- 
v.ances made in the production of very 
high-frequency o.soillations of consid- 
erable power for radar purposc.s sug- 
gT'.'itcd to the American physicist L. W. 
Ah •arcs the possibility of making a 
linear accelerator capable of yielding 
high-c-nergy protons. In the apparatus 
const nteted at Berkeley, California, in 
1917, ('scillations of .about 200 million 
cycles per second frecpioncy arc em- 
ployed in extremely short bursts, or 
pnht^s. The lengths of the c^ylindrical 
drift tubes vary from four to thirteen 
inchc<. Protons of about 4 Mev en- 
crp>', nbtainefl from a Van de .Graaff 
fl'-rt '•o'^tatic generator (§■ 9.381. are in- 
tmduct'd into t!u> nceclenitor and their 
cjtergy U steadily incro.a.'ted to 32 Alev 


227 

as they pass from one end to the other, 
a distance of about 40 feet. 

9.60. When the plans for the new 
linear accelerator were being made in 
1946, it was hoped to construct seven 
sections which w’ould bring the energy 
of the protons up to nearly 300 Mev. 
This is several times the maximum 
value previously obtainable in other 
ways, and it seemed that higher en- 
ergies could not be attained by these 
methods because of the relativistic in- 
crease in mass of the particles at high 
speeds (§ 3.63), as will be explained 
below. However, later theoretical de- 
velopments showed how this limitation 
could be overcome, and so the. plans 
for the seven-stage linear accelerator 
have been shelved. The existing ap- 
paratus, capable of jdelding 32 hlev 
protons, is nevertheless valuable, for, 
like the electrostatic generator, it can 
produce a strong, well-defined beam 
of ions, such as is required for scatter- 
ing experiments. 

9.61. Another device, also called a 
linear accelerator, but operating on a 
different principle, has been designed 
by the American physicist W. W. 
Hansen at Stanford University, for 
producing electrons, as distinct from 
positive ions, of high energy', A copper 
tube is divided into a number of sec- 
tions by means of disks, with holes in 
the center, placed at increasing inter- 
vals along the tube. Pulsed oscilla- 
tions of extremely high* frequency are 
introduced, and the wave length of a 
given phase is determined by the dis- 
tance between the disks in the tube. 
Since these distances increase regu- 
larly, the wave length, and hence the 
phase velocity, also increases, the fre- 
quency remaining constant. Electrons 
entering the tube with the forward 
pha.‘:e of the wave alwaj-s remain in 
phase with the traveling wave and 
steadily increase in cnerg>'. In the 



228 


Sourcebook on Atomic Energy Chap IX 

first, 12-foot model of the linear elec- interest than any other was a direct 
tron accelerator, built in 1947, enei^cs outcome of the earliest form of the 
up to 6 Mev were obtained, but an litujar accelerator Instead of using 
instrument, 160 feet m length, capable shielding (or drift) cylinders of grad 
of producing electrons of 1000 Mev ually increasing length as the speed 
energy is planned * of the charged particles became greater, 

9 62 Several linear accelerators, op- E O Lawrence, of the University of 
eratmg on a similar principle, to be California, conceived the idea of using 
used for producing electrons of very a magnetic field to make the particles 
high energy, are being planned or are move m a spiral of increasing radius, 
under construction at the Massachu- so that the length of the path auto- 
setts Institute of Technology, and at matically increased with the speed of 



H r PorcNT 


I n 

Fio 0 6 Simplified representation of cyclotron with two dees 

other laboratories in the United States, the accelerated particle The first re* 
at the Telecommunications Research port of the idea was made by E 0 
Establishment in England, and else- Lawrence and N E Edlefson at the 
where These devices are being made meeting of the National Academy of 
possiblelargelyoivingtotheuseofmag- Sciences held in Berkeley, Cabf, in 
netrons, which_are high-energy power September 1930, and the first expen 
sources, developed during World Warll mental accelerator, using the new prin- 
for the production of ultra bigh-fre- ciple, was constructed by E 0 Lw- 
quency microwaves, that is, radar rence and M S Livingston m 1931 
waves, of about 10 cm wave length The instrument, which has grown tre- 
raendously m size and power since that 
The Cyclotron tune, is now known as a ajclotron] 

9 63 The method for producing pos- ^Vhile the original model produced pro- 
itively charged particles of high eneigy tons with energy of 80,000 ev, the 
which has attracted more world-wide latest type, completed in 1946, yields 

• At the end of 1949, a 14-ft unit had accelerated electrons to 25 Mev, the frequency e® 
ployed was 2855 megacycles per sec 

t In 1935j E 0 Lawrence, E McMillwi and R L Thornton wrote ‘ Since we shall have 
many occasions in the future to refer to this apparatus, we feel it should have a name THe 
term ‘magnetic resonance accelerator 13 the word ‘cyclotron ' of obvious 

derivation has come to be used as a sort of labimtory slang ” By 1936, however the name 
cyclotron, because of its convenience, had come into general use 


229 


The Acceleration of Charged Particles 


deul'jrons of nearly 200,000,000 ev, 
i.c., 200 Mev, and alpha particles with 
nearly twice this energj*, A modifica- 
(ion reported in 1949 makes it also ca- 
pable of producing protons %nth about 
350 energy. 

9.54. In its most general form, the 
cyclotron consists of two fiat, semi- 
circular boxes, called dees because of 
their .“^hape, which are indicated by 
Di and Dz in Fig. 9,G, I. These are 
surrounded by a closed vessel, con- 
taining gas at low pressure, placed be- 
tween the poles of a magnet as showm 
in the elevation in Fig. 9.6, II. A high- 
frequency, alternating potential, of sev- 
eral million cj'cles per second, is ap- 
plied between the dees, which act as 
electrodes. At S an electrically heated 
filament produces a stream of electrons 
which causes ionization of the ga-s, 
hydrogen, deuterium or helium, con- 
tained in the sj'stem; hence, S may 
be regarded as a source of positive 
ions, namely, protons, deuterons or 
alpha partic!c.s, respectively. 

9.55. Suppose that at anj' p.artic- 
ubir instant the direction of the al- 
ternating jiolentinl is such that the 
eler{ro<lc Di is positive and Dz is neg- 
ative. A positive ion starting from 
the source S will then be attracted to 
Dz, but as a uniform magnetic field 
acts in a direction at right angles 
(lug. 9.G, II), the ion will move in a 
circular path. Tim radius of this path 
e.an l}e readily deri\'cd from equation 
12.7) v.hioli, a.s stated earlier, applies 
to all tyj)es of eUarged particles in a 
macumtie field; the result is 


uiirre n is tlie mass of the ion, c is 
it* charge, v its velocity, and H is the 
of the nuignetic field. 

9.5'D. N\hile it is in the interiur of 


the dee, the speed of the ion remains 
constant, just as it does udthin the 
cylindrical drift tubes of the linear 
accelerator (§ 9.46). But after describ- 
ing a semicircle through Dz, the ion 
reaches the gap between the dees \vhere 
it becomes subject to the action of the 
applied potential difference. If the os- 
cillation frequency is such that in the 
time of passage through Dz the sign 
of the potential is reversed, so that 
Di is negative and Dz is positive, the 
positive ion wdll now be accelerated 
toward Di. Since its energy is oonse- 
quently greater than it was originally, 
the ion will move faster, that is, v will 
increase; hence, the circular path in 
jDi, under the influence of the magnetic 
field, will have a larger radius r, as 
can be seen from equation (9,1). 

9.67. The striking and significant 
property of the cyclotron is that the 
time taken by the charged particle to 
traverse the semicircular path in the 
dee is independent of the velocity of 
the particle or of the radius of the 
path. That is to say, the increase in 
length of the path, due to the larger 
radius, is exactly compensated by the 
increase in the velocity of the particle. 
The length of the path is ttt, where 
r is the radius, and tt has its usual 
significance; since r; is the velocity, 
the time T taken to traverse the semi- 
circle is given by 


r 


Upon substituting the value of r from 
equation (9.1), it is seen that 



i which is independent of both v and r. 
i 9.58. This meaim Uuat if the ascilla- 



230 


Sourcebook on 

tion frequency is adjusted to the nature 
of the given ion and to the strength 
of the magnetic field, the charged par- 
ticle will always keep m phase with 
the changes of electric potential be- 
tween the dees Thus, each time the 
particle crosses the gap from Di to 
JDj it will receive an additional impulse 
toward D}, on the other hand, when it 
crosses from Da to Di, it will be ac- 
celerated toward Di, for the direction 
of the potential will then be reversed 
The result of these repeated impulses 
IS that the energy of the ion is steadily 
mcreased, and at the same time it 
describes a flat spiral of increasing 
radius Eventually, the ion reaches 
the penphery of the dee and it can be 
brouj^t out of the dee chamber by 
means of a deflecting plate at P (Fig 
9 6, I) which IS charged to a high 
negative potential The attractive force 
actmg on the positive ion draws the 
latter out of its spiral path, so that 
it can be used to bombard any desired 
material 

9 59. Althou^ the foregoing de- 
scnption has referred to a single ion, 
actually the source S supphes ions con- 
tmuously, so that a stream of high- 
energy ions will emerge from the cyclo- 
tron The value of the maximum en- 
ergy may be calculated by making use 
of the fact that it is energy of motion, 

1 e , kmetic energy, and is consequently 
equal to where m is the mass 

of the particle and ti is its tna Yimum 
speed when it leaves the dee Accord- 
ing to equation (9 1), v is equal to 
Her/m, and if ij is the rathus of the 
dee, the maximum velocity, at the 
penphery, will be HeR/m The kinetic 
energy E of the ion as it emerges from 
the cyclotron will then be 

(93) 

'^ \ m ) 2 m 

9 60. If the oscillation frequency of 


Atomic Energy Chap IX 

the potential is adjusted to the partic- 
ular ion, the maximum energy attain, 
able will be determined by the product 
If, for a given cyclotron, i e , ^ 
IS constant, the magnetic field strength 
H IS also mamtained constant, it fol- 
lows that the energy which a charged 
particle wU attain is proportional to 
the square of its charge, and inversely 
proportional to its mass Protons, for 
which e and m are both unity in terms 
of electromc charges and atomic wei^t 
units, respectively, will thus acquire 
the same energy as alpha particles, 
with c equal to two and m to four units 
I>euterons, on the otherhand, forwhicb 
e 18 unity and m is two, attain 
only half this maximum energy 
9.61. The time for the ion to traverse 
any semicircular path is given by equa- 
tion (9 2), and so the time to make a 
complete turn of the spiral is twice 
this quantity, that is, 2TmlHe 
frequency h> of the oscillations required 
to keep the ion m phase is the recipro- 
cal of this quantity, so that 


and upon combimng this result with 
equation (9 3) , the energy of the emerg- 
ing ion IS found to be 

D = 27r^ie’w*m. (95) 

9 62. As a general rule it is more 
convenient to operate the cyclotron 
with the field strength H constant, as 
implied above, but an alternative pos- 
aibihty is to raamtain constant the 
oscillation frequency w of the voltage 
supply to the dees, and to adjust the 
magnetic field to satisfy equation (9 4) 
for different particles. It can be seen 
from equation (9 5) that, in contrast 
to the case m wbch the magnetic field 
» constant, the maximum energy will 



231 


The Acceleration of Charged Particles 


now he proportional to the mass in 
of the particle, and independent of 
its charge. Under the conditions of 
constant o'^cillator fiequency, the en- 
erg)' attainable by an alpha particle 
will then be four times, and that of a 
denteron twice, that of a proton. 

9.63, Attention may be called to the 
fact that the voltage applied to the 
decs does not appear in cither equation 
(9,3) or (9.5), so that the maximum 
cnerg}' which a given charged particle 
can acquire in a particular c 3 ’’clotron 



I'lo, 9.7. The fust cj’clotron, about 11 
inches diameter; the magnet is not shown. 


is independent of this voltage. The 
rc.ason is that when (he voltage is small 
the ion mahes a largo number of turns 
before in.'schingthe periplierj', but when 
die voltage is high the nunrber of turns 
is small. Tire product, rvhich deter- 
mine.; the total energy', is the same in 
each cas.e, provided the magnetic field 
// and the m.axinmra radius R of the 
path are unchanged. 

9.64. No matter how the cj'clotron 
i- opomted, it can be seen from equa- 
tion {9.3) that "the maximum cnergr- 
ac'i'.iimi by a given particle i.s deter- 
by H-R-, j.c., i)y the square of 
the priKluct of the field strength and 
tta radium, or diameter, of the dec. 

I*.!*"'' ’“.’iw.fo r Ilf rbt' poh’ fsces b t 

rychtrem’' smplv an ia,<tn 3 r 

c.-.n- *rr 3;.,-, ft a 9 iv inchc... Icf'v 


It is evident, therefore, that in order 
to obtain ions of higli energj' it is 
necessaiy to increase the strength and 
size of the magnet in the field of which 
the ions traverse their spiral path. The 
first cyclotron (Fig. 9.7) to jdeld high- 
energ 3 ' charged particles us.able for nu- 
clear transformations, built by Law- 
rence and Livingston of the University 
of California in 1931, had a magnet with 
pole faces 11 inches in diameter and 
this produced protons of 1.22 hlev en- 
ergy. Subsequently, instruments with 
27-inch, later extended to 37-inch, and 
60-inch diameter pole faces* were con- 
structed Law'rence and his collab- 
orators in Berkeley, Calif., and several 
C3mlotrons were erected in other parts 
of the world, the majority being in the 
United States. 

9.65. Prior to 1946, the most ener- 
getic particles available were deuterons 
of about 20 Mev and alpha particles of 
40 Alev cnerg 3 '’ obtained from the 60- 
inch Berkele 3 ’’ C 3 '’clotron, emplo 3 dng a 
magnet w'eighing about 200 tons. Al- 
though the c 3 ^clotron is capable of pro- 
ducing strong beams of high-energy 
ions, the voltage is neither as constant 
nor as uniform as it is for those from 
the other 131)65 of accelerators described 
above. The c 3 mlotron is a powerful 
inslniment for certain investigations 
requiring i)articles of ver 3 " high energy, 
but where the exact value of this energ 5 " 
need not be precisel 3 ’' known. How- 
ever, by passing the emergent beam 
through a magnetic field it is possible 
to .‘^ort out ioms having definite Energy 
values, if required. 

The Syxchrocyclotron' 

9.66. After the completion of the 
00-inch r-yclotron in 1939, LawTcnce 
considered the possibility of designing 

'fd to (ies':rii)C the of the cyclotron. Tha? 
ent with pole fnres 60 inches in diameter; the 



232 

an instrument of much greater power 
which would not only be able to brmg 
about new types of nuclear rearrange- 
ments, but might be capable of actu- 
ally creating particles by converting 
energy mto mass Encouraged by the 
gift of over a million dollars from the 
Rockefeller Foundation, which was aug- 
mented by funds from other sources, 
work on the construction of the new 
cyclotron was commenced m Berkeley, 
Calif , m August, 1940 It was to 
have a magnet containing 3700 tons 
of steel and 300 tons of copper, with 
pole faces 184 inches in diameter, and 
was to be capable of acceleratmg deu- 
terons to 100 Mev and alpha particles 
to 200 Mev However, this giant mag- 
net was destined to play another role 
before it finally took its mtended place 
in the world’s largest cyclotron 
9 67. It will be recalled (§ 8 92) that 
in 1941 Lawrence had become mter- 
ested in the separation of the iso- 
topes of uramum by the electromag- 
netic method After preliminary stud- 
ies with the magnet of the 37-mch 
cyclotron had shown the procedure to 
be feasible, work on the 184-mch mag- 
net, which had been set aside, was 
resumed and it was completed m May 
1942 Durmg the summer of the same 
year an apparatus employing the new 
magnet produced the fii^ significant 
quantities of fairfy pure uranium-235 
It was the success achieved m this 
manner that led to the decision to 
erect a large-scale electromagnetic sep- 
aration plant at Oak Ridge, Tenn , as 
stated in Chapter VIII In 1945, the 
giant magnet was released from its 
wartime services m connection with 
the separation of isotopes and restored 
to ite ongmal purpose, the production 
■jof high-energy ions, after a lapse of 


Chap IX 

nearly four years But the delay waa 
not altogether without compensation 
for, the discovery of a new principle 
made it possible for the 184-mch cyclo- 
tron to yield particles with twice the 
amount of energy originally expected 
9 68 When concluding, from equa- 
tion (9 2), that the tune taken for a 
given charged particle to describe the 
semicircular path m either of the dees 
of a cyclotron is mdependent of the 
velocity of the ion or of the radius of 
the path, the tacit assumption was 
made that the mass m of the particle 
remained constant For energies of 
the order of 10 or 20 Mev, this is 
substantially true, but at higher en 
eigies, and hence higher speeds, the 
relativistic mass effect (| 3 69) becomes 
important The value d the mass m 
IS given by equation (3 8), and this 
increases rapidly as the velocity v of 
the particle approaches the speed of 
Lght A deuteron of 20 Mev energy, 
which IS the fastest-movmg particle 
produced m the 60-mch cyclotron has 
a velocity about 0 145 times the speed 
of hght, and its effective mass, by 
equation (3 8), is 1 01 times the rest 
mass The change of mass is compara 
tively email, and so the operation of 
the cyclotron is not greatly affected 
9 69 At higher energies, the mass 
of the particle mcreases to such an 
extent that its effect becomes appreci- 
able * It can be seen from equation 
(92) that as the mass of the ion m 
creases, bo also does the time T of 
transit throu^ the dee As a result 
the particle will no longer be m phase 
with the oscillating potential Instead 
of reachmg the gap between the does 
at the exact instant required for it to 
receive an accelerating impulse, the 
ion will arrive too late and conse- 


It was suggested by W W Hansen (see 5 1) 50) that when the speed of the particles sp* 
preaches that of hght and an increase of energy results in an appreciable increase of 
rather than of velocity, the device should be called a jxmderator, instead of an accelerator 


Sourcelooh on Atomic Energy 



233 


The Accdcraiion of Charged Parlides 


qacntly will gain little or no additional 
cnergw On account of the relativistic 
inas^j increase, therefore, an approxi- 
mate limit is set to the energj^ that 
can be acquired by an ion in a conven- 
tional cyclotron operating xmder given 
conditions. In order to offset this lim- 
itation to some extent, it was pro- 
posed, when the 18'1-inch cyclotron 
was firet planned, to use a ver}’ high 
potential— about a million volts — so 
that the ions would need to make only 
a comparatively small number of turns 
in order to attain higher energies. 

9.70. In 1945, V. Vclosler in Rus- 
sia and, a few month.s’ later, E. Ivl. 
Mci^Iillan in the United States, inde- 
pendently, .showed that allowance could 
lie made for the effect of the increase 
of mass of a particle moving at high 
speeds so as to keep it in phase with 
the oscillating potential.* Two meth- 
ods of compensation are possible. One 
is to increase the magnetic field H in 
proportion to the mass, so that in/H 
jvmains constant; it can be seen from 
Wluatiou (9.2) that the time T would 
then be unaffected by the increase of 
ma.s-:. Tlje other possibility, which is 
more readily adapted to the cyclotron, 
is to leave the magnet ic field unchanged, 
b\U to dccre.n.so the frequency of the 
(XN'ciliating potential as the mass of 
the particle incrca.«c 3 . 

9.71. In this connection, McMillan 
pomterl out that if the oscillation fre- 
quency is continuously adjusted so as 
to coincide noth the decreasing fre- 
quency of rotation of the particle, as 
the time T increases, the principle of 
P'mr^ dnlnUtij c-an be utilized. This 
principle m.ay be explained by refer- 
ence to Fig. 9.8, which represents the 
varintmn with time of a cycle of the 
lugh-frequoncy oscillating potential. In 


normal operation the charged particle 
receives its acceleration at a point indi- 
cated b}’’ the time to, just beyond the 
potential peak. If the particle always 
remained exactly in phase, it would 
always arrive at the appropriate time 
fo of the cycle to gain the proper amount 
of energx'. However, if the particle 
arrives too late, for example at the 
time ii, the potential will then have 
decreased, so that it null not receive 



Fig, 9.8, Diagram to illustrate the prin- 
ciple of phase stability. 


the regular increment of energy, and 
hence of mass. It follows from equa- 
tion (9.2) that the time T required 
to traverse the path will be less, and 
consequently its next arrival udll be 
in time for it to receive the full ac- 
celerating effect of the potential at to. 
On the other hand, if the particle 
reaches the accelerating position too 
soon, at time to, for example, it will 
gain more energx’- and mass than nor- 
mal, since the potential is now higher 
than .at to. It will thus take a slightly 
longer time to return to the point 
where it receives the next impulse. 
The rotation of the charged particles 
is thus automatically s 3 Tichronized with 
the changing frequency of the acceler- 
ating potential. The action is similar 
to that in a symehronous motor, and 
hence the name simchrolron was pro- 


in Wt7 that essentially the .«'amc idea had been 
Energy in 1913 in connection -oith a proposed 
nccilrrating prtitoK.'! (I 9.97). ' ‘ 



234 5oi(rce6oofc on Energy Chap JX 

posed by McMillan for a device using charged particle enters or leaves the 
this principle dee, it acquires additional energy, &o 

972 About SIX months after cwi- that it follows a spiral path just as if 
struction of the 184 inch cyclotron had two dees were emplojed By means of 
been resumed m 1945, it was decided ft rapidly rotating, variable condenser 
to modify the instrument 6o that the the frequency of the oscillating potea 
frequency of the oscillations could be tial applied to the dee is decreased bo 
vaned to compensate for the increase as to compensate for the gam m the 





















Fig 9 9 The 184-inch synchrocyclotron in the University of California Radiation 
Laboratory, Berkeley, Calif 

of the mass of the accelerated ions at 1 effective mass of the particle as its 


high speeds For this reason the ma- sp 
chine (Fig 9 9) is referred to as a or 


speed increases A 200-Mev deuteron 
or ft 400-Mev alpha particle has a 


syncfiTocyclolron or as a freguency-mod- speed of about I 4 X 10^“ cm per see 
uCafed cyc!o(ron It uses a single dee, or about 0 47 times the velocity of 
instead of two dees as in the conven- light It follows, therefore, from equa 
tional cyclotron,* the oscillating po- tion (3 8) that the mass is 1 14 times 
tential being applied between it and or 14 per cent greater than, the rest 
a ground connection Every time a mass at Zow energies The frequency 

* It may be mentionpd that the 11 inch cydotron which was the first to produce useM 
acceleration also bad only one dee 0'^ ® H As a general rule one dee electrode fan be 
used ^hen the applied potential is not too hi^ fhc other terminal of tho oscillator is then 
grounded 




235 


The Acceleration of Charged Particles 


of the oscillator must consequently de- 
crease in the same proportion if the 
charged particles are to be kept in 
phase wth the alternating potential 
Tvhich causes the acceleration. 

9.73. It is apparent from equation 
(9.2) that the time for a charged parti- 
cle to traverse the dee does not depend 
solely on the mass m, but rather on 
the ratio of the mass m to the charge 
c of the i6n. This ratio has the same 
value for deuterons {vi = 2, c = 1) 
as for alpha particles (m = 4, c = 2); 
hence -with a given oscillator, the same 
frequency modvilation can be used for 
both of these ions. For this reason, 
the Berkeley sj-nchrocyclotron, which 
went into operation in November 1946, 
was at first employed for the accelera- 
tion of deuterons and alpha particles. 
But early in 1919, the completion of 
anew oscillator, with a dual frequency 
range, made it possible to obtain high- 
cnergy protons, in addition. For deu- 
terons and alpha part iclos the frequency 
i.s modulated from 11,5 million c 3 'cles 
per .sec., at the instant of injection, 
to 9.8 million cj’clos per .sec., wlien the 
ions re.'ich the peripherj' of the dee. 
In this manner about 200-hIev deu- 
terons and 400-hIev alpha p.articles 
have l>een produced. In the higher 
froquencj' range, the oscillator is mod- 
ulated from 23 to 15.9 million cimlcs 
per fee,, and this is u.'^ed to obtain 
proton-s of 350 hlev energj*.* In each 
there are about si.vtj' pulses of 
high-frequenej' oscillntion.s per second. 

0.74, There is one slight difference 
between the output of a cj'clotron and 
that of a synchrocj'clotron which is 
worthy of mention. In the former the 
flow of accelerated ions is regarded as 
contimmus, although it actualh' con- 
of a series of piilse.s corresponding 


to each half-cycle of the oscillating 
potential. For a frequency of 10 mil- 
lion cycles per second there would thus 
be 20 million pulses in this time inter- 
val. In the sjmclirocyclotron, however, 
the pulses are much less frequent, since 
they occur at the rate of only about 
si.xty per second. The operation of 
this instrument is such that a pulse 
of ions is carried from the ion source 
at the center to the periphery of the 
dee as the frequency of the oscillating 
potential is decreased from its initial 
to its final value in a one-sixtieth part 
of a second. The frequency then re- 
turns to its original value and another 
pulse of ions is earned from the source 
to the peripher 3 ^ This procedure is 
repeated sixty times cverj’’ second while 
the sjmchrocyclotron is in operation, 
and so the output consists of a series 
of p\ilses emerging at this frequency. 

The Betatron 

9.76. The discussion in the preced- 
ing sections has referred mainly to the 
acceleration of positive ions, since these 
are of prime importance in connection 
with nuclear transformations. Never- 
theless, for certain purposes, such as 
the production of penetrating X-rays 
of high energj', it is desirable to obtain 
beams of energetic electrons. Both the 
voltage multiplier (§9.36) and the 
Van de Graaff electrostatic generator 
(§ 9.39) can be used to accelerate elec- 
trons, but the energies are limited to 
a few million electron volts. The lin- 
ear type of accelerator, mentioned in 
§§9.50, 9.51, however, holds out the 
possibility of producing electrons of a 
billion electron volts energy. 

9.76. The cyclotron, on the other 
hand, cannot be readily adapted for 
use with electrons because of the large 




236 


Sourc^oh on Aiormc Energy Chap IX 


relativistic increase of mass at fairly 
low energies This happens because 
the rest mass of the electron is very 
small, compared with that of a proton 
or a deuteron, hence it must attam a 
much higher speed in order to cany 
the same amount of kinetic enei^ 
At 1 Mev energy, the speed of an 
electron is more than nme-tenths of 
the speed of light and the relativistic 
mass 13 2 5 times as great as the rest 
mass In its present form even the 
synchrocyclotron could not be adapted 
to make allowance for such large in- 
creases of mass, although the possi- 
bility that this might eventually be 
achieved cannot be entirely ignored * 
9.77 The idea of using magnetic 
induction to accelerate electrons was 
considered by R Wideroo m Germany 
m 1928, and by E T S Walton m 
England m 1929, but their attempts 
to put it into practice uere not suc- 
cessful In 1936 the German physicist 
M Steinbeck secured a patent for an 
induction instrument wth which he 
claimed to have obtained electrons of 
1 8 Mev energy, although the beam 
intensity was admittedly small The 
first successful induction accelerator 
with an appreciable output of electrons 
was designed and constructed by D W 
Kerst m the Umted States in 1940 To 
this he gave the name betatron, because 
it was used for pJeetiTons which are, of 
course, identical with beta particles 
(§ 2 98) The first betatron gave elec- 
trons with 2 3 Mev energy, but this 
was soon followed by one yielding 20- 
Mev electrons, constructed by Kerst 
m conjunction with the General Elec- 
tric Company at Schenectady, N Y 
Subsequently, the latter organization 
constructed a 100-million volt instru- 
ment, this was completed m 1943, al- 
though details of its operation were 
not released until 1945 Several other 
• A 5-Mev electron cyclotron has been budt 


betatrons have since been built for 
vanous purposes 

9.78 The action of the betatron n 
based on the same fundamental pnn- 
ciplcs as that of the familiar trans- 
former in w hich an alternating current 
applied to a primary coil, induces a 
similar current, usually with a higher 
or lower voltage, m the secondary wind 
mgs The effect is due essentially to 
the production by the alternating pn- 
maty current of a time-variable mag- 
netic field which, m turn, induces an 
oscillating current, that is, an oscil- 
latory flow of electrons, in the second 
ary coil In the betatron the secondary 
is an annular, i e , ring-shaped, evac- 
uated glass tube, often referred to, for 



Fig 6 10 Schematic seetional diagram of 
a betatron 

obvious reasons, as the “doughnut,” 
showm in section at AA in Fig 9 10 
This IS placed between the poles of a 
specially shaped electromagnet B, en 
ei^ized by alternating, pulsed current 
passing tlxrcuj^gb the roils CC One 
purpose of this magnet is to produce 
a strong field m the central space or 
“bole” of the doughnut, and hence it 
IS constructed ^vlth a large amount of 
iron m the core Electrons are pr(> 
duced from a heated filament, and 
these are given a prehmmary accehra- 
tion by application of an electric fiew 
havmg a potential difference of 20,000 
to 70,000 volts Even with the com- 
paratively low energies thus acquired, 
the electrons travel at very high speeds, 
la Canada 


237 


The Acceleraikm cf Charged Parlicles 


from one-fifth to nearly one-half the 
velocity of light. 

9.79. Tlic variation vith time of the 
magnetic field strength, in a single 
cycle of the alternating current which 
energizes the magnet, may be repre- 
sented by the sine-wave curve in Fig. 
9.11. As the field strength starts to 
incrc.ise, i.c., near the point 0, the 

p.arlly accelerated electrons are injected 

into the doughnut. The effect of the 
growing magnetic field in the central 
space is to induce an electromotive 
force, or voltage, within the douglinut, 



Fkj. 9.11. Single cj'clc of sine-wave varia- 
tion of m.agnetic field used in the betatron. 

which incrca.scs the energy of the mov- 
ing electrons. Since they are traveling 
in a magnetic field, the electrons are 
forced into a ctirved path, but instead 
of being a spiral, as in the cyclotron, 
the increasing magnetic field keejis them 
moving in a circle of constant radiiis. 
Bcforcnce to equation (9.1) wll show 
th.at thi.s is possible provided the field 
strength H grows proportionatelj' to 
the increase in the product of the mass 
m and the velocity v, i.e,, to the in- 
eraase in the momentum, of the elec- 
trons. Thu.s, the electrons are kept 
moving around the doughnut in a fairly 
rtable, cirtnikar ])ath, cnergv' Iwing ac- 
<iuinxl in e.ach Lap or turn. 

9.80. When the field strength has 
rvached the point P in Fig. 9.11, where 
5l c<-asc-< to increase and will subse- 


quently decrease, a pulse of current 
is sent through an auxiliarj^ coil which 
suddenly changes the magnetic field. 
As a result the high-energj'- electrons 
are displaced from their stable path 
and fall on a target, for the production 
of X-rays, or the electron beam may be 
made to leave the apparatus and used 
for other purposes. 

9.81. If the electrons had not been 
removed at the point P, the decreasing 
magnetic field from this point on would 
have induced an electromagnetic force 
in the opposite direction to that act- 
ing between 0 and P. This would 
have the effect of slowing down the 
previously accelerated electrons. Con- 
sequently, only the first quarter of the 
cycle is actually used for acceleration 
purposes, injection of electrons being 
always made at the point 0, while 
removal occurs at P in each .cycle. 

9.82. A simple calculation will show 
how it is possible for the betatron to 
produce electrons ndth very high en- 
ergies. As seen above, the electrons 
when introduced into the doughnut 
are already mo\'ing wth speeds ap- 
proaching that of light, and this is 
further increased as the electrons ac- 
quire additional energy. It may be 
assumed, therefore, tliat the average 
speed of the electrons between injec- 
tion and removal is tw'o-thirds the 
velocity of light, i.e., 2 X 10*® cm. per 
see. The diameter of the circular path 
within the doughnut of a large beta- 
tron may be taken as 300 cm., so 
that the electrons will travel this path 
rougWy 2 X 10*®/300, i.e., 6.7 X 10' 
times per second. 

9.83. If the frequency of the alter- 
nating current used for the magnetic 
field is 60 cycles per second, the time 

; for one cycle is 1/60 sec.; hence, the 
j quarter cycle from 0 to P, dviring which 
the electrons are accelerated, lasts 
I rouglih' 1/240 sec. During tliis period 



238 

the electrons make 6 7 X 10^/240, i e , 
280,000 turns of the circular path m 
the doughnut If the electrons acquire 
an average of 250 ev of energy in each 
turn due to the electromotive force 
produced by the magnetic field chang- 
ing vith time, they uill have a total 
energy of about 70 Mev 
9 84 In the General Electric 100- 
miUion volt betatron, the diameter of 
the doughnut is about 180 cm and the 
magnet weighs 135 tons The electrons 
travel around the doughnut 250 000 
times, covering a distance of about 
900 miles between mjection and re- 
moval and gaming 400 ev of energy 
at each turn The 100-Mev electrons 
have a velocity which is more than 
99 99 per cent of the speed of light, 
and their relativistic mass is nearly 
200 times the rest mass 
9 86 Since the operation of the beta- 
tron IS unaffected by the increasing 
mass of the electron as it gams energy, 
It at first appears that extremely high 
eneigiies might be obtainable by means 
of this device However, it has been 
shown theoretically that a charged par- 
ticle such as an electron, moving m a 
circle, as it does m the doughnut of 
the betatron, will lose some of its en- 
ergy m the form of radiation The 
effect of this phenomenon, which was 
confirmed experimentally m the Gen- 
eral Electnc Research Laboratory in 
1947, IS to set a limit to the energy 
which the gyrating electrons can ac- 
quire The energy lost m each turn 
of the circular path is proportional to 
where E is the energy of the 
electron and r is the radius of the path, 
hence the amount lost increases very 
rapidly as the energy E becomes larger 
Eventually, the electron loses just as 
much energy in the form of radmU(m 
as it gains from the electromotive force 


Chap JX 

due to the tune changing magnetic field 
ra each turn around the doughnut * 

9 86 Two possibihties present them 
selves for minimizing the loss of en 
ergj by radiation Since this is deter 
nuned by E*/r, one solution to the 
problem is to employ a larger dou^ 
nut, so that the radius r of the electron 
path may be increased The other 
measure which could be taken is to 
decrease the number of turns the elec 
trons make between mjection and re- 
moval, by altermg the magnetic field 
so as to permit the acquisition of a 
greater amount of energy m each turn 
A large instrument based on these prui 
ciples, and employing a magnet weigh 
mg 1000 tons, is being constructed by 
Kerst, the inventor of the betatron, 
at the University of Illinois It is ex 
peeled to yield electrons with 300 Mev 
energy 

The Electron Synchrotrov 

9 87 An alternative, and in many 
ways simpler, procedure for conferring 
high energies upon electrons is to make 
use of the synchrotron principle enun 

ciatedindependentlym 1945 by Veksler 
and by McMillan, as mentioned m 
§ 9 70 The first practical application 
of the idea is claimed by F K Goward 
and D E Barnes, m England, who 
m 1946 converted a 4-Mev betatron to 
yield 8-Mev electrons Shortfy there- 
after, m 1947, H C Pollock and W F 
Westendorp of the General Electric 
Company designed and built a machine 
combining the action of both betatron 
and synchrotron It produced elec- 
trons of 70 Mev energy, although the 
magnet weighed only 8 tons, as com 
pared ivith 135 tons of the lOO-Mev 
betatron 

9 88 A somewhat similar device, ca- 
pable of yielding 330-Mev electrons 


• This limitation does not apply to the linear deetron accelerator (J 0 50), aince the electron 
does not lose energy by radiation when moving in a straight line 


Sourc^jook on Atomic Energy 



hn 5 been built by McMillan in the Radi- 
ation Laboratory at Berkeley, Calif, 
lliis instrument con.sists of an evacu- 
ated annular tube, or doughnut, shown 
in plan at A in Fig. 9.12, between the 
poles of a magnet energized by alter- 
nating (pulsed) current, as in the beta- 
tron. But, in the electron sjmehrotron 
the magnet has cjdindrical, i.c., ring- 
shaped, poles, and it docs not e.\-lend 
into the central space or hole of the 
doughnut. For this reason, the sjm- 
chrotron magnet is much lighter than 
that of a betatron having the same 
cnergj' output.* In place of the central 


The Acceleration of Charged Parlicloi 239 

9.89. In the operation of the sjm- 



— A 


Fm. 9.12. Diagrammatic plan of portion 
of a sjnichrotron. 

portion of the magnet, there are a 
small number of iron b_ars B, called jffHx 
bars, which serve an equivalent pur- 
pose, b\it onb’ to a limited c.\‘tent. In 
addition the interior of one of the 
eight segments, of which the doughnut 
i.s con.structed, is coated with copper C, 
leaving a narrow gap G, near one end, 
to fonn what is luiown as a resonant 
(fii’ii'j. A grounded o-scillator, produc- 
ing an alteniating potential of 3000 
Volts mn.ximum, at the constant liigh 
frequency of 47.7 million cycles per 
sef'ond, is connected to C. Wien the 
o-elllator is turned on, a charged parii- 
ele receive.^ approximately 2000 ev of 
caesp,- each time it pas.=:es the accel- 
enunig gap, provided it is in phase 
v'ith the oscillat loirs. 


chrotron, electrons produced bj-- a 
heated tungsten wire are injected into 
the doughnut after being given a pre- 
liminarj' acceleration by means of an 
electrostatic field of about 90,000 volts. 
Due to tlie action of the increasing 
magnetic field, the electrons travel in a 
circular path, and the change with time 
of the field through the flux bars in- 
duces an electromotive force within 
the doughnut which adds energy to 
the electrons, just as in the betatron. 
However, the number of flux bars is 
such that when the energy of the elec- 
trons has reached about 2 Mev, the 
bars have become magnetically sat- 
urated, and are no longer able to in- 
duce an electromotive force; betatron 
operation then ceases. 

9.90. At tliis point, the constant 
high-frequency, oscillating potential is 
applied to the resonant cavity C, and 
sjmehrotron action commences. Ad- 
ditional energy is now acquired by the 
electrons each time they pass the ac- 
celerating gap G. If the potential 
applied to C operates at the proper 
frequency, as will be described shortly, 
the electrons are kept in phase and 
receive an increment of energj’’ in each 
revolution. These increments are larger 
than those in the betatron, and so the 
electrons can acquire a higher energy 
in the same, or smaller, number of 
turns. 

9.91. At 2 Mev energjq wlien sjTi- 
chrotron operation is initiated, the ve- 
locity of the electrons is already 97.9 
per cent of that of light. Since they 
cannot exceed, or even attain, the speed 
of light, it is cwdent that the subse- 
quent increase of velocity cannot be 
more than about 2 per cent. Conse- 
quently, as the energx- of the electrons 


is increa.sed from 2 Ivlev to SQO Mev, 
-^VV-Mcv noaferromapr.ftk sj-achrotron, in wlueh tho in.'icnctic field is produced by 
‘■'-rreni ibroudi Fperially vle'^iened coil*, U lieinK constructed by the General Electric 
v '-Tiiwny sn eix)jvjrat!on v-ith the Office of Naval Research. 



242 Sourcebook on 

(Bev) range, the name betatron has 
been suggested for the latter * 

9 98 The choice of protons for the 
particles was largely determined by 
the fact that they can acquire very 
high energies without losing appreci- 
able amounts by radiation as do elec- 
trons The loss of energy of a charged 
particle per revolution is proportional 
to E*/r, as stated in § 9 85, but it is 
also inversely proportional to the fourth 
power of the rest mass of the particle 


Atomic Energy Chap IX 

the whole of the region m which the 
particles spiral around, consequentlj 
the pole faces must be large In the 
synchrotron, on the other hand, a nng 
shaped magnet surrounding an annular 
tube or doughnut is all that is required 
The estimated total weight of theinag 
bet m the Berkeley bevatron is about 
10,000 tons, compared with 4000 tons 
for that of the 184-inch cyclotron ca- 
pable of producing particles with about 
one-twentieth of the energy 



Fig 9 13 Schematic drawmg of the bevatron 


Since the mass of the proton is nearly 
two thousand times that of an electron, 
the former will lose as much energy 
per nsfcidftjii in an orbrd of given cadnts 
at 6 Bev as an electron does at 3 Mev, 
and this is known to be negligible 

9 99 The decision to use the syn- 
ehrotron principle for acceleration, so 
that the particle moves in a circ^ar 
path of almost constant radius, rather 
thrn the cyclotron, where the path is 
a spiral, means that the magnet can 
be much lighter in proportion In the 
cyclotron, the magnetic field must cover 

• The scientists at Brookhaven Laboratory . 
produced will have energies of the same ordia 
ase of this term would avoid possible confusio 


9 100 In its general form, and m 
fact m its principle of operation, the 
Berkeley bevatron is to be similar to 
dfre JV/arfirgsiT syaehratim 
above It will consist of four quadrants 
of about 50-foot radius, joined by short- 
straight pieces about 20 feet long, as 
represented diagrammatically in Fig 
9 13, 1, the elliptical, or flattened, cr^ 
section of the doughnut DD is indi- 
cated m Fig 9 13, II The magnet 
M, M, which consists of a large num- 
ber of plates approximately 9 feet 
across, arranged side by side, surrounds 

tivor the name cosmotron. because 
as those m cosmic rays (Chapter XVIi) 

1 between bevatron and betatron 


243 


The Acceleralion of Charged Particles 


only the quadrants of the doughnut, 
alternating (pulsed) current being used 
for energizing purposes. Protons, pre- 
viously accelerated to about 10 Mev 
cncrg>' by means of a linear accelerator 
or a cyclotron,* Tvdll be injected at A, 
in one of the straight portions of the 
douglinut, and after having had their 
cnergj’ increased, as a result of many 
rotations, they will be removed by a 
deflector at B. Injection and removal 
■will thus take place outside the mag- 
netic field. 

9.101, Tlie accelerating device C, 
equivalent to the dee of the cj’’clotron 
or the resonant cavity C (Fig. 9.12) 
of the sjuichrotron, is also inserted in 
one of the straight portions, outside 
the influence of the magnet; it is con- 
nected, as usual, to a source of high- 
frequency alternating potential. Some- 
what different types of electrode are 
planned for the Berkeley and Brook- 
Itavcn proton synchrotrons. 

9.102, After the protons are injected, 
they will gain energy, probably in the 
amount of over 1000 ev per revolution. 
In order to keep them moving in a’ cir- 
cular path of essentially constant radius 
in the doughnut, the field strength of 
the quadrant magnets will be increiUsed, 
as in the electron sjmehrotron. Since 
.a proton does not attain a velocity 
within a few per cent of that of light 
until its cnergj' is about 3 Bev, it is 
npp.arcnt that up to this point allow- 
.'mce will have to be made for the 
i^teadily incrc.osing speed with which 
the clmrged particles gjvate, as tlie 
strength of (ho magnetic field grows. 
3 he time required for the protons to 
nunke one turn of the doughnut will 
p.‘w.iurilly decrease .‘^o that the num- 
W of tum.s per tnut time, i.o., the 
5n.%qucney of revolution, vill increase 
C'trrt-'.pondingly, To maint,ain the con- 

* Icr t}:^ BroDiiJwen co.^molron, injection 
^ |r?’'f:cr5tor. 


dition of phase stability, which is es- 
sential for proper synchrotron action, 
the frequency of the high-frequency 
alternations applied to C must be in- 
creased in the same manner. The rate 
at which the frequency is changed will 
have to be very accurately coordinated 
vith the increasing magnetic field so 
that the particles maintain an orbit of 
constant radius. 

9.103. The frequency wiU be in- 
creased fairly rapidly at first, as the 
protons gain speed, but the rate will 
be slowed dovm and the frequency 
will become almost constant tow'ard 
the end of their passage, as the speed 
approaches that of light. Tlie period 
during which the magnetic field strength 
increases, and the frequency of the 
oscillations applied to C increases cor- 
respondingly, will last approxirnatcly 
one second; there will then be a short 
delay to permit the magnet to recover, 
follow'ed by another period in wiiich 
the protons gain energy. The output 
of the bevatron will thus consist of a 
series of pulses, at intervals of about 
si.v seconds. In each pulse a proton 
will make nearly four million revolu- 
tions and will travel some 270,000 
miles! The intensity of the emergent 
beam, as measured by the total num- 
ber of protons present, will not be 
large, and the voltage, although high, 
will not be verj’- uniform. These prop- 
erties are also characteristic of the 
sjmchrocyclotron. A convenient fea- 
ture of the proton sjmehrotron is that 
by suitable adjustment of the ejec- 
tor B, the beam can be removed at, 
approximately, any desired energj' re- 
quired for particular e.xperiments. 

9.104. In order to provide a test 
for the basic design principles to be 
incorporated in the Berkeley proton 
Kj'nchrotron, a quarter (linear) scale 

will probably be from p. 4-Mcv Van de GraafI 



250 Sourceboc3e on 

among the vanous product nucbde% 
and the formation of [soZn*®] by the 
interaction of Zn” with a neutron, 
1 e , IS, the reverse of process (2), has 
been observed There is no doubt that 
with alpha particles of sufficient eneigy 
reaction (5) could also be reversed, as 
could the others if the appropriate 
target nuclei were available 
10 19. In the interaction of an ac- 
celerated deuteron with the Cu*‘ nu- 
cleus, process (3), m which a proton 
IS emitted, predominates at low deu- 
teron energies, for a reason which will 
be given in § 10 28, but this becomes 
less important at higher energies, when 
reactions (3) and (4) occur at the same 
time It IS important to note that at 
suitable energies several nuclear reac- 
tions can take place simultaneously, 
although one particular process often 
predonunates at low energies and an- 
other at high energies Consequently, 
the method of formation of the com- 
pound nucleus may have an mdirect 
influence on the nature of the sub- 
sequent process For example, when 
[soZn®] B formed from Zn*’ and a 
neutron of low energy, by the reversal 
of process (2), the only reaction which 
can take place to any appreciable ex- 
tent IS the radiative capture process 
(1), the relatively small amount of 
excitation energy is thus emitted as a 
gamma ray \^en produced m this 
maimer, the compound nucleus [soZn®] 
has insufficient energy for anj of the 
other reactions mdicated above to be 
possible When high-energy neutrons 
are used as the incident particles, in- 
stead of those ivith low eneigy, some 
of the other reactions occur It appears 
that whenever a compound nucleus 
has enough energy to make expulsion 
of a material particle possible, the 
probability of gamma-ray emission is 
extremely small 


Atomic Energy CAap J 

Thansmutation by Protons 
10 20. In the precedmg sectioiis & 
discussion has been given of the gen 
eral prmciples underlymg transmuta- 
tion processes, m which a compound 
nucleus is formed as an mtermediate 
stage In this and the following sec- 
tions reference will be made to specific 
cases of nuclear reactions with vanom 
projectiles, and some additional mat- 
ters will be elucidated 
10.21. With protons as the mcident 
particles, radiative capture processes 
1 e , of the (p, 7 ) type, have been ob- 
Krved for a number of the lighter 
elarofinfs, thus, 

which may be written as Al” (jj,7) Si® 
The product is a nuclide with both 
atomic number and mass number one 
unit higher than those of the target 
matenal Other instances of the same 
kind are Li^(p, 7 )Be*, N^*(p, 7 ) 0 '‘j 
'F*’(p, 7 )Ne«’ and Cr«'(p, 7 )Mn» Tk 
bombardment of lithium by protons 
has been used os a source of high- 
energy (17 Mev) gamma radiations for 
expenmental purposes 

10 22. As may be anticipated, the 
probability of the (p,n) type of reac- 
tion is relatively high, provided the 
proton has sufficient energy to pen^ 
irate the energy barrier and fonn a 
Compound nucleus Such a reaction is 

uNa” + jH' iiMg“ + (!«', 

where the neutron emitted is repre- 
tented by on* since it carries no charp 
but has a mass number of umty on the 
atomic weight scale The product nu 
feleus IS seen to have the same mass as 
the target element but its atomic num- 
ber IS one unit higher Several (pi'v 



251 


Nvckar Transmutatmi and Ariifmal Uadioacimiy 


reactions are known, although they 
arc more common with the ligliter than 
with the heavier elements, since higher 
energies are ncccssarj’’ for the nuclei 
of the latter to bo penetrated by the 
protons. 

10.23. For the s.akc of completeness, 
it may be mentioned that reactions 
of the ( 7 ), 2 ?!) and (p,pn) types have 
been observed when using high-energj’ 
protons. In view of the results ob- 
tained with other })articlc.s of very high 
energy, in the range of .several hundred 
million electron volts, there is no doubt 
that protons can initiate reactions in 
whieli three, four or even more particles 
are emitted. 

10.24. Nuclear proco.s.sc.s of the ( 7 ),a) 
and {p,d) types, where the particles 
ex])e}letl arc an alpha particle and a 
deuteron, rc.spoctively, arc compara- 
tively muatmmon l)ecausc of the small 
probabilitj' of jjenctrallng the rela- 
tively high energy burriens. The large 
Ijinding energy of the alpha ])articie 
(§ 4,40) makc.s its cmissioti more likely 
than that of a dcttlcron, hut in any 
event, unles-H high-energy protons arc 
u.'-ed, (ho ip, a) reaction is to be ex- 
pected only with target elements of 
low .atomic number fur which (he elcc- 
tn>-!iit}r n’pul.‘''ion is not too high. The 
hrsT tnmsmulation proco.'^ involving 
arnheially ncoelerated particles to be 
discovered (§ 0.21) wa.s of the (p,a) 
type, namely, Lih'p,n)Ho*; another e-x- 
ample is 

-h ..H> - eC" -f -Hcb 

< >ne of the rare e.'ws of a (p^d) reaction 

~ sH' -» -b iH', 

b';i th*'n* an- probably special circtnn- 
ubirn fnvur the emission of a 
dv'U’ nm in lbi< 


10.26. A few instances have been 
recorded of reactions of the {p,v) tj’Pe, 
in wliich a proton is both the incident 
and the emitted particle; the product 
nucleus must then have tlie same mass 
number and atomic number as the 
target element. The only difference 
between target and product nuclei is 
that the latter is in a higher energy 
(excited) level than the former, tlie 
incident proton being deprived of some 
of its energy before it, or another pro- 
ton, is ejected. An example of this 
kind of reaction, which is one instance 
of the more general phenomenon of 
nuclear cxciiaiion, is 

In«5 + iH' + jHS 

where the asterisk (*) is used to indi- 
cate an excited state of the In“^ nu- 
cleus; the excited nucleus eventually 
loses its excess energy as gamma radia- 
tion. It is not certain that nuclear 
excitation processes always involve the 
intermediate fonnation of a compound 
nucleus, because the {pjn) process might 
be expected to occur preferentially. 
There is a possibility that the inter- 
action between the electric fields of 
the target nucleus and a high energy 
proton, or other charged particle, may 
result in the transfer of energj' from 
the latter to the former in a close 
encounter without the necessity of ac- 
tual fu.sion. 

10.26. Irrespective of mechanism, 
the fonnation of an e.xcited state of 
the target nucleus, accompanied by the 
expulsion or repulsion of a particle of 
the .same kind a.s the incident parti- 
cle, with docrea.sed kinetic energj’^, is 
often described as weladic .‘^c-attering. 
In clnsfic i^caUcrimj, on the other hand, 
kinetic energy may be, and generally 
is. Iniusfcrnxl from the projectile to 
the target nucleus, but the latter i.s 



252 


Sourcebook on Atomu: Energy 


not raised to an excited state of higher 
internal energy 

Transmutation bt Deutehons 

10 27. It was seen in § 10 9 that 
the deuteron is a particularly effec- 
tive projectile for causing nuclear trans- 
mutations because a relatively small 
amount of energy, about 2 Mev, is 
sufficient to cause its rupture into a 
neutron and proton This small bind- 
ing energy of the constituent nucleons 
of a deuteron has another significant 
effect in facilitating nuclear changes 
In the course of a study, reported m 
1935, of reactions of the (d p) t3T3e 
resulting from the bombardment of 
various elements i^ith deulerons ac- 
celerated by means of a cyclotron, 
E 0 Lawrence, E M McMillan and 
R L Thornton m the United States 
noted that the efficiency of the proc- 
esses mcreased with increasing energy 
of the mcident particle* at a rate that 
was appreciably greater than was to 
be expected from the wave-mechamcal 
theory of barrier penetration by the 
deuteron (§ 9 19) 

10 28 An explanation for this be- 
havior was immediately proposed by 
the American mathematical-physicist 
J R Oppenheimer who, in conjunction 
with M Phillips, derived certain theo- 
retical consequences which were found 
to be in complete agreement ^vlth 
the observed facts According to the 
Oppenkeimer-Pkilhps mechanism, the 
deuteron behaves as a relatively loose 
combmation of a neutron and a pro- 
ton, since the bmdmg energy is com- 
paratively small When the deuteron 
approaches a nucleus, the electrostatic 
repulsion of the positive charges tends 
to force the proton away, while the 
neutron is not affected J£ the eneigy 
of the incident deuteron exceeds the 


Chap X 

neutron proton binding energy, i e 
about 2 Mev, the proton portion will 
break off and be repelled, but the neu 
iron will enter the target nucleus, since 
there is virtually no barrier to prevent 
this taking place In a sense, the 
Oppenheimer-Philhps type of process 
may be regarded as occumng m two 
stages the break up of the deuteron 
mto a proton and a neutron, followed 
by the reaction between the latter and 
the target nilcleus The resultmg com 
pound nucleus usually does not ha\e 
sufficient energy to eject a particle, 
but if it IS in an excited state it will lose 
its excess energy in the form of gamma 
radiation 

10 29 Nuclear reactions of the (dp) 
type are quite common, for they have 
been observed with nearly all elements 
At low deuteron energies the mecha- 
nism IS presumably as described above 
but at high energies it is probable that 
as m most transmutations, a compound 
nucleus is formed by combination of 
the whole deuteron with the target 
nucleus, followed by the ejection of a 
proton The end result is, of course, the 
same ns in the Oppenheimer-Phdhps 
processes Examples of (d,p) nuclear 
transmutations, which mclude elements 
of low, medium and high atomic weights 
are given below It wll be observed 
that the product is always an isotope 
of the target element, with a mass 
number one unit higher 

,LiT + iH* ,Li« + iH‘ 

«Cd‘» -f- 4- jH‘ 

mBi*“ -f iH‘ 

1030 Attention may be called to 
the last of these reactions, m which 
the product is an isotope of bismuth, 
of mass number 210 and atomic num- 


• The variation with the energy of the incident particle of the efficiency, or yield, of a au 
clear reaction is called the exctlalton fttnOum of particular process 



253 


Ntidcar Transmuiation and Artificial RadioaciivUy 


her 83. Reference to the table in § 5.51 
and Fig. 8.1 will show that these are 
the mass number and atomic mimber 
of the naturally occurring radioactive 
element commonly known as radium E. 
bombardment of ordinary bismuth by 
accelerated dcuterons docs, in fact, 
jicld a product which is identical wdth 
mdium E; it emits beta particles and 
has a half life of 5.0 days. 

10.31. Another {d,p) reaction of spe- 
cial interest was discovered by Ruther- 
ford, in conjunction with M. L. E. 
Olipliant and P. Harteck, in 1934, as 
a rc.s\ilt of the bombardment by deu- 
tcroiKS of deuterium itself, in the form 
of a solid compound. The process thus 
involvc.s the interaction of an accel- 
erated deutcron with a stationary one, 
and the result is the emission of a 
proton, leaving a third isotope of hy- 
drogen, of mass number 3, as the resid- 
ual nucleus; thu.s, 

,IP -!- iIP -f J-P, 

wlicre tH* is ttie new isotope which 
lias been called (ritinm.* The additiv- 
ity of the subscripts, indicating the 
nuclear charges or atomic numbers, 
show.s that the prorluet, tritium, has 
an atomic nuralmr of unity, and hence 
must be isotopic with hydrogen. Tlie 
atomic weight ha.s Ijccn determined 
from the iaiown isotopic weights of 
deuterium and hydrogen, and the reac- 
tion cnci’gj' Q derived from the en- 
ergy' of the deutcron projectile and the 
ranges of the resulUmt particlc-s. The 
value of Q is -{-3.9S Mev, which is 
equivalent to -f-0,0042S mass unit, and 
t.'ildng the isotopic weights of deute- 
rium^ and hydro^n as 2.01472 ancT 
re.spoctivcly, the isotopic 
weight of tritium is found, by tire 


method described in §9.33, to be 
(2 -f 2.01472) - (1.00813 -f- 0.00428), 
which is 3.01703. It will be seen later 
that tritium is unstable and does not 
occur naturally; consequently, it can 
be obtained only in nuclear transmuta- 
tion processes. 

10.32. Competing with the proton- 
emitting nuclear changes induced by 
deuterons of moderate energies, are 
reactions of the (d,n) type, in w'hich 
the deutcron enters the nucleus of the 
target element and a neutron is then 
ejected from the resulting compound 
nucleus. A large number of transmuta- 
tions of this land have been reported; 
in several cases, especially mth target 
elements of low atomic rveight, partic- 
ularly berjdlium, high-energj’’ neutrons, 
useful for e.vpori mental purposes, are 
emitted. Among reactions of the (d,n) 
type are the following; 

aLi® -}- iH.* — > ^Be^ -j- ou’ 

kTc»® - f iH* -fon» 

-h g^Po-'o + onh 

In each case the mass number and 
atomic number of the product are both 
one unit lugher than those of the target 
element. In the third example quoted 
above, the product has the mass num- 
ber and atomic number of naturally 
occurring polonium, or radium F; its 
identity with the latter has been proved 
by a study of the radioacthity observ’ed 
after bombardment of bismuth with 
deuterons. Both radium E, resulting 
from the (<i?,p) reaction, as mentioned 
earlier, and nadiuni F, from the (d,n) 
process, arc obtained simultaneously 
at moderately high (7 to 10 Mev) 
deutcron energio.s, 

10.33. In addition to producing tril- 


by Rnnlopy with deuterium, from deuieroi fsoeond). A 
t u-prcr.entcd by iho T, Rnd the oucleu., called a triton, h 



254 


SouTCtbooh on Atomic Energy Chap X 


jura, the interaction of deuterons with 
deuterons is accompanied by the for- 
mation of an isotope of helium of mass 
number 3, by the reaction 

+ iH® sHe* + onS 

which IS a (d,n) process This helium 
isotope IS present to a very minute 
extent in ordinary helium gas By 
making use of the energy change Q 
of the H*(d,n)He* reaction, and the 
known masses of the neutron and the 
deuterium atom, the isotopic weight 
of He® 13 found to be 3 01702 

10 34 When the mcident deuterons 
have high energies, of the order of 
10 Mev or more, two neutrons are 
expelled from the compound nucleus, 
le^ing to a number of reactions of the 
(d,2») type with target elements of 
moderately high mass numbers, thus, 

ssTeW + iH® -♦ ijCoW + 2on* 

tiTe'*® + iH> sjiwo + 2on* 

At still higher energies, such as have 
been obtained by means of the 184-mch 
cyclotron (§9 72), reactions of the 
(d,3n) type, and others of a still more 
involved nature, have been observed 
The subject of disintegration by very 
high energy particles ivill be considered 
separately m a later section (§ 10 55 
e< seq ) 

10 36 Because of the high nuclear 
potential energy barrier for alpha par- 
ticles, which mcreases with the atomic 
number of the target nucleus, reactions 
of the (d,a) type are observed only 
with deuterons of high energy and ele- 
ments of fairly low atomic number 
One example is 

ssCa« + + jHe*, 

and others are Li*(d,tt)He*, Ne“(d,a)F“ 
Mg*®(d,o!)Na** and Ni“(d,a)Co“ 


10 36 Although they are as unex 
pected as the (p,d) reactions referred 
to m § 10 24, a few instances are known 
of processes of the analogous (d,t) type 
where t represents the triton, or nucleus 
of tntium, 1 e , of H® or T, the third 
isotope of hydrogen One case, namely, 

4Be* + iH® 

indicated in brief by Be®(d,0Be®, is of 
especial interest since the bombard 
raent of berylhum by 10 Mev deuter 
ODs has been used as a source of high- 
energy tritium nuclei (§ 10 52) 

10 37. Possibly due to the fact that 
there is a considerable gam of energy 
when a deuteron enters a nucleus, radi- 
ative capture (d,y) and nuclear excita- 
tion (d,d) reactions are less common 
The excitation energy of the compound 
nucleus is so high that it can very 
quickly emit a neutron, at least, or 
even a proton The probability of the 
relatively slow (d,d) and (d,Y) reac- 
tions IS therefore small 

Tbanbmutation b\ Alpha Pabticleb 
10 38 It will be recalled (§ 9 4) that 
Rutherford first observed m 1919 the 
transmutation of the nitrogen atom 
as a result of interaction with alpha 
particles from radioactive sources The 
nuclear reaction he discovered was of 
Tithwib OF 

elements of low atomic number As 
the latter mcreases, the potential bar- 
ners preventmg the entry of the alpha 
particle and the emission of the proton 
become higher and the probabilitj of 
the (a,p) process decreases Howexer, 
with the availability of artificially ac- 
celerated alpha particles (helium ions), 
this reaction, which Rutherford was 
not able to observe for elements above 
potassium, has now been detected for 
nuclei with high atomic numbers 



255 


Nuclear Transmutation and Artificial Badioaciivity 


10.39. Although it was not realized 
until 19.32, the (a,n) reaction, which, 
incidentally, led to the discovery of 
the imdron (§2.111), frequently oc- 
curs at the .same time as the {ct,p) 
change. An important example of an 
{«,n) transmutation is 

Jlc’ + :lle’ -> cC'- -f ouS 

which i>rovidos a useful laboratory 
source of neutrons; alpha particles of 
sufficient energy are obtained from 
radon gas, that is, •from radium em- 
anation, or from r.adium itself. By 
tisiug energetic alpha particles, (a.n) 
reactions have been observed with the 
hcavie-st elements, including uranium, 
and the artificial elements neptunium 
and i»hitonium (Chapter XV). 

10.40. When the energ}’ of the alpha 
particle is sufficiently great to pene- 
trate a highly charged nucleus, other 
reactions, such as («,2n), {a,np), {a,Zn), 
(cr,4n) and (a.Znp), in which two or 
more ituclcons arc expelled, tnkc place. 
Nuclear processes occurring with inci- 
<icnl alph.a particles of verj' high en- 
erg%' will be referred to in § 10.55 and 
in Chapter XV. 

10.41. Alpha particles are able to 
bring about miclear excitation reac- 
tions of the (a, a) type, as a result of 
inehistic scattering, but, like the an- 
alogous (p,p) and (d,d) processes, they 
are not common. The emitted alpha 
particle h.ns a lower cnergj’ than the 
ineideut particle, leaving the target 
luirlcns in an excited high-energ}' slate, 
luu unoh.'ingcd in mass niimber and 
.atomic mnnb'-r. 9’hc indium hotopc 
oi juas< nu5nl>cr 11.5 can be exciteci 
by alpha particles, a.s well a-s by pro- 
tons tf 10.25), acconiing to the reac- 
tion In*”(«,a)In*’-*. A few other elc- 
tivnk* Can be ntised to higher nuclear 
enrig;,' staters in the same manner. 


Tbakbmtjtation by Neutrons 

10.42. The production of neutrons 
of various energies and their properties 
n-ill be described more fuUy in Chap- 
ter XI, and so only brief consideration 
will be given here to transmutation 
reactions induced by neutrons. The 
most common type of process is radi- 
ative capture, represented by {n,y), 
in which a neutron is taken up by the 
target nucleus and the resulting com- 
pound nucleus then emits its excess 
energy as gamma radiation (§ 10.14). 
Neutrons of relatively low energjq fre- 
quently called slow neutrons, are partic- 
ularly effective for the (n,y) reaction, 
an instance of which is 

59Cu“ -f otd — > + y. 

Virtuall}' all the elements, except some 
of the verj' lightest, exhibit radiative 
capture of slow neutrons; the product 
is always isotopic nith the target ele- 
ment, but its mass munber is one unit 
higher. 

10.43. With fast neutrons, that is to 
say, nitli those ha\’ing higher energies, 
the {n,p) tyqje of reaction is fairly 
common; adchtional energy is here re- 
quired to permit the proton to escape 
from the compound nucleus. Such re- 
actions are N *'‘(7i,p)C“ and CP(n,'p)S®^, 
so that the product nucleus has the 
same m.ass, but its atomic number is 
one unit less than that of the target. 
For elements of atomic number of about 

i 40 or le.ss, and in a few instances where 
I the atomic niunbers are higher, (n,a) 

I reactions have been obsen’ed; exam- 
ples arc F’nR,a)N>® and Zn'TR,a)Ni'=*. 
If the neutron energy exceeds about 
8 Mev, processes of the (n,2r?) type, such 
as G‘Tn,2«)C“ and Hg»=’(n,2n)Hg’^, 
become possible; the product is here 
isotopic v.'ith the target element, as in 
the {n,y) reactions, but its mass num- 



258 


Sourcebook on 

■which, have some features in common 
■with the Oppenheimer-Philhps {d,p) 
reactions (§ 10 28) The tnton con- 
sists of two neutrons and a proton, 
and it was considered that, under the 
influence of the electrostatic field of 
the tai^t nucleus, the proton is re- 
pelled leaving a temporary combina- 
tion of two neutrons, called a dineutron, 
the possible existence of which was 
suggested by M H Colby and R T 
Little m 1946 The uncharged di- 
neutron would then readily enter the 
target nucleus, just as does the residual 
neutron m the Oppenheiraer-PhiUips 
reaction Some experimental evidence 
for the formation of the dineutron («n*) 
in the bombardment of tritium by ac- 
celerated tntons, according to the reac- 
tion 

iH* + ,He‘ + cn\ 

was reported m 1950 from Los Alamos, 
by A Hemmeadinger The conclu- , 
sions, however, await confirmation 

10 63 In 1939, L W Alvarez and ! 
R Comog showed that the hebum-3 | 
isotope was present to a very small ' 
extent in ordmary hehum, by usmg | 
the Berkeley cyclotron (§ 9 63) as an ' 
electromagnetic separating device At | 
the same time they obtamed evidence i 
Ssff" ibo i'siwhv® *4i5<- 

other process of the same type, namely, 
H*(He®,p)He*, ivas studied in 1943 by 
the Purdue group mentioned above, 
in which accelerated He* ions were 
used to bombard deuterium More 
recently, the reaction N‘*(He*,a)N** 
has been observed, both mcident and 
ejected particles are isotopes of helium, 
so that the product is isotopic with, 
but has one unit of mass less than, the 
target nucleus 

10 64 A few observations have been 
made on the bombardment of vmious 


Atomic Energy Ckap X 

tai^ets by accelerated lithium and car 
bon ions, but the results are mdefimte 
Because of their relatively high charge 
and mass, these ions have a 
probability of penetrating an atomic 
nucleus unless they have extremely 
high energies Little attention has hith 
erto been paid to this aspect of nuclear 
transformation, and the use of rela- 
tively heavy and highly charged pro- 
jectiles 13 a field of investigation that 
may perhaps attract interest in the 
future 

Fission and Spallation 

10 66 It will be noted that m the nu 
clear transmutation processes already 
considered there are only a few cases 
of reactions associated with the expul 
Sion of more than one particle In the 
great majonty of mstances there is 
either radiative capture, when no ma- 
tens] particle leaves the compouod 
nucleus, or else a single particle is 
emitted As a result, the products are 
very close, both m mass number and 
at6mic number, to the target elements 
Tins 18 , on the whole, to be expected 
because the bindmg energy of a nu 
cleon 13 about 8 Mev, and hence an 
mcident particle whose energy is of 
the order of 10 Mev is unlikely to bnng 
about the ejection of more than one 
or two neutrons or protons But if 
/as.rtMifes AD JB siS>o.TgX sa.v 

in the region of 100 Mev or more, 

were employed, transmutations of other 
types, m which there were consider 
able differences between target and 
product nuclei, might be anticipated, 
and such reactions have mdeed been 
observed 

10 66 It may be mentioned that the 
Bohr theory of the capture of the inci 
dent particle, followed by redistribu- 
tion of its energy among the nucle- 
ons of the resulting compound nucleus 

(§ 10 ll),requiresmodificationforpro- 



259 


Nuclear Transrmiiaiion and Ariificial RadioacUviiy 


jcctiles of higli cncrg>'. Because of its 
higli speed, such a particle can often 
pass through the target nucleus, being 
dcpri\'ed of a fraction only of its en- 
ergy' (§ 11.109). Atomic nuclei are thus 
somewhat "transparent” for highly- 
cnergetic projectile-s. 

10.57. The first of the high-energj’- 
transmutation processes to be consid- 
ered Is that known as ficsion, in w'hich 
the target nucleus, in addition to emit- 
ting a small number of nucleons, usu- 
ally neutrons, breaks up into two nu- 
clei of approximately equal size. The 
phenomenon of fission forms the basis 
of the practical utilization of atomic 
nuclear energy, and so it will be dis- 
cu.s^ed more fully in Chapter XIII; it is 
mentioned here only for the sake of 
completeness. Actuallj’- the first in- 
stance of fission W'as not brought about 
by particles of high energy, but by slow 
neutrons interacting with the uranium- 
235 isotope. The more abundant ura- 
nium isotope of mass number 238 
undergoes fission w’hen subjected to tho 
action of fast neutrons, of energy ex- 
ceeding I hicv. Other nahirally occur- 
ring elements of high atomic number, 
p'.ldi as thorium and protoactinium, can 
l>o split by neutrons in a similar man- 
ner. Fission of uranium and thorium 
has been induced by protons, deulcrons 
and gamma rays of energy less than 
10 Mev, and also by 32-hIev alpha 
particles 13.17). In the process of 
fia-ion the nucleus of the target cle- 
fnent breaks into two fragments in 
many different waja; thus, about sixty 
'ndth mass numbers from 
72 to 15S, have been detected in 
the fresion of uramum-235. However, 
th'* great majority of these products 
tall luui two groups with mnss num- 

in the range of S5 to 101 and 
130 to PSP. 


10.68. The examples of fission given 
above refer to the hea\dest elements 
and do not actually represent veiy- 
high-energj’' reactions, but the use of 
particles of higher energj^ has made it 
possible to induce fission of several 
somewhat lighter nuclei. Alpha parti- 
cles accelerated to 400 Mev energy 
by the 184-inch sjmcbrocyclotron have 
been, found to cause fission of bismuth, 
lead, thallium, platinum and tantalum, 
while 200-l\Iev deuterons are similarly 
effective for bismuth, lead and thal- 
lium. Neutrons of 100 Mev energy 
produce fission of bismuth, lead and 
other heavy nuclei. A considerable 
number of nuclides of lower atomic 
weight have been detected among the 
products. It may be mentioned here, 
although the matter will be treated 
more fully at a later stage, that fission 
of uranium by particles of very high 
energy leads to an entirely different 
distribution of products from that ob- 
sciwed in fission with neutrons of lower 
energy. 

10.69. Another phenomenon, w'hich 
differs from fission in having been de- 
tected so far only with particles of 
high energ}', was discovered in 1947 
by G. T. Seaborg, I. Perlman and their 
collaborators at the Radiation Lab- 
oratoiy', Berkele.y, California, using the 
facilities of the 184-inch cyclotron. 
When elements in the intermediate 
range of mass mxmber and atomic num- 
ber arc bombarded by 400-Mev alpha 
p.article3 or by 200-Mev deuterons, 
thej'^ do not undergo fission and brciik 
up into tw'o, more or less equal, parts. 
Instead, such nuclei emit various num- 
bers, up to about twenty or thirtj', or 
even more, of nucleons, le.aving a series 
of products of lower mass and atomic 
number, llie name spallalian* has 


been proposed for reactions of this kind. 




SouTcehook on Atomic Energy 


or more groups, those m each group 
have the same energy, but the energies 
of the various groups are different. In 
the reaction five groups of 

protons have been detected, and m 
Al*^(a,p)Si®® foursuch groups have been 
observed It is probable that the emis- 
sion of each group of protons leaves 
the product nucleus in a different en- 
ergy state When the protons of max- 
imum energy are expelled the product 
IS presumably in, its loivest nuclear 
energy level, that is, m the ground 
state Each group with successively 
smaller energy corresponds to a suc- 
cessively higher energy level of the 
product nucleus When the latter is 
m one of these excited states it will 
return to the ground state emittmg, 
at the same time, gamma radiation 
If the arguments presented here are 
correct, the energy of the radiation 
should correspond to the difference m 
energy oftwo proton groups By study- 
ing the recoil electrons produced by 
the radiation (§6 5), this expectation 
has been confined 
10 69 The results described above 
provide information concerning the en- 
ergy levels of the compound nucleus 
and of the product nucleus, respec- 
tively Advantage has been taken of 
nuclear excitation processes, due to 
indastic scattering of protons (§ 10 25), 
m particular, to throw light on the 
energy levels of stable target nuclei 
A beam of protons of known eneigy 
IS allowed to impinge on a given target 
matenal, and the number scattered at 
a defimte angle is examined 1^ means 
of a proportional counter or a Geiger- 
MuUer tube (Chapter VI) By inter- 
posmg absorbing materials, the num- 
bers of protons having vanous energies 
can be determined In this way, it is 
found that certain characteristic en- 
ergies predominate among the scat- 


tered protons The difference between 
these values and the mitial energy be- 
fore scattering represents the energies 
of excitation for various levels of the 
target nucleus 

Nuclear Cross Sections 

10 70. The efficiency or probability 
of a nuclear reaction can be defined 
m terms of the number of particles 
emitted, or of nuclei undergoing trans- 
mutation, for a specified number of 
mcident particles A more general, uni- 
form method, which baa been widely 
adopted, is to express the relative effi- 
ciency by means of a quantity called 
the nuclear cross section It represents 
the effective area of cross section of a 
single nucleus of a given species for a 
particular reaction Thus, when the 
efficiency of the process is high, the 
so-called nuclear cross section will be 
large, on the other band, when the 
efficiency is low, the cross section will 
be small 

10 71. If J IS the number of incident 
paiticles Btnking m a given tune a 
1 sq cm area of the target material, 
containing N target nuclei (or atoms), 
and A is the number of these nuclei 
which undergo transmutation in the 
specified tune, then the nuclear cross 
section < 7 ,* expressed as sq cm per 
nucleus, is defined by 

<r = ^ sq cm per nucleus (10 1} 

10.72 The description of <r as a nu- 
clear cross section may be justified m 
the followmg manner Suppose <r sq 
cm 13 actually the area per nucleus 
effective for a given transmutation 
process, since the matenal of the target 
surface contains N nuclei (qr atoms) 
per sq cm , the effective area per 
sq cm of total surface is consequently 


• Greek’n^a this symbol 13 invanably used to represent nuclear reaction cross sections 


263 


Nudcar Ttdtismvlcilion and Arlificial Hadioacliviiy 


aN sq. cm. In other words, aN is the 
miction of the surface which is capable 
of taking part in the transmutation 
rwiotion; this also represents the frac- 
tion of the incident particles 1 falling 
on the target surface which twll be 
involved in the process. The number 
actuallj' reacting is thus cNI, and this 
will he equal to A, the number of 
target nuclei undergoing transmuta- 
tion, so that 

.4 = crAT. 

Comparison of this result with equa- 
tion (10.1), which provides the formal 
definition of <r, shows the two to be 
identir.al. Hence, it is justifiable to 
regard cr as the effective cross section 
of a single nucleus for a given nuclear 
it'action. 

10.73. Since A is the number of tar- 
get nuclei reacting, while N is the 
total number of such nuclei per sq. 
cm., the quanthj' A/N is the number 
of nuclei, and hence of incident parti- 
clc-s, taking part in the process per 
single target nucleus. Upon dividing 
by the total number I of particles 
falling on 3 .'?q. cm. of the target, the 
result A/NI, which is equal to <r, by 
oqu.ntion (lO.l), is the fraction of the 
p.artirlcK falling on 1 sq. era. of target 
th.at intcr.act with a single nucleus. 
'I 111 ? jT-presents a useful .alternative 
definition of the cross section avhich 
brings out its relationship to the effi- 
eicney of the nuclear reaction; ob\n- 
cnir-ly, the larger the fraction of the 
incident particles reacting, the greater 
in the yield or eniciency of llie proce.ss. 

10, fd. Hje value of the nuclear crass 
p=-vlion de;H'nds not only on the nature 
I'f the targt't element, but also on the 
part icular rt'action undcrconsidcration, 
asid the cnerg>- of the- incident particle' 


A given nucleus, such as Li', for ex- 
ample, tvill in general have differ- 
ent cross sections for the reactions 
Li"(p,n)Bc’ and Li'(p,«)He^ which oc- 
cur simultaneously. The values rep- 
resent the probabilities of the two 
processes for protons of a specified 
energjq and the ratio will usually change 
with the energy of the incident par- 
ticles. 

10.76. When the nuclear cross sec- 
tion for a particular reaction is re- 
quired, it is necessaiy to determine the 
number of nuclei taking part, either 
b}’’ counting the particles, such as neu- 
trons or alpha particles, respectively, 
wliich are expelled, or by determining 
the number of product nuclei formed. 
Both of these methods have been used 
in different instances. On the other 
hand, if it is sufficient to Icnow the 
total nuclear cross section for all proc- 
esses in which the incident particles 
are absorbed, a simple procedure is 
possible. If lo is the number of inci- 
dent particles falling in a given time 
on 1 sq, cm. of the target material, 
wliich is in the form of a sheet of 
tliickness x cm., and I is the corre- 
sponding number of these particles 
wliich emerge from the other side of 
the sheet, the difference h — I ha\’ing 
been absorbed in various nuclear re- 
actions, then 

Y = c-A'", (10.2) 

io 

where A’’ is now the number of target 
nuclei per cc., c is the base of natural 
logarithms and cr is the total nuclear 
cross section. Hence, it is possible to 
determine the latter from measure- 
ments of the intensity of the beam of 
incident particles before and after pas- 
sage through the target material.* 


* rV r furi* 


i *1 arrangcrticale nccciisary for tljc inclusion or exclusion of scat- 



264 


Sourcebooh on Atomic Energy 


10 76 Experimental values for nu- 
clear cross sections are usually in the 
vicinity of 10“” to 10-^^ sq cm per 
nucleus, although in exception'll cases 
the results may be extremely small* 
or they may be as high as 10“*® sq cm 
per nucleus The average diameter of 
a nucleus can be taken to be about 
10~‘* cm , and so the actual area of 
cross section is approximately 10“** 


Chap X 

sq cm Since this represents the order 
of magnitude of many nuclear reac- 
tion cross sections, a umt, called a 
6am, equal to 10“** sq cm per nu 
cleus, has been adopted f Thus, nu 
clear cross sections are frequently m 
the range of 0 001 to 1 bam, but they 
are known to vary from 10~» (or less) 
to 10* bams for different reactions 


ARTinCIAL RADIOACTIVITY 


Radioactive PnoDUcra of 
Nucleah Processes 
10 77 In the earlier experiments on 
nuclear transmutation, the process oc- 
curring was usually inferred from the 
nature of the emitted particle, special 
usebeingmadeofcloud-chamberphoto- 
graphs m this connection Because nu- 
clear reactions are generally performed 
on such a small scale, m companson 
with the quantities commonly involved 
m moat chemical work, the identity of 
the product could not be determined 
by conventional methods Even mass 
spectroscopic procedures were hardly 
adequate to deal with the minute 
amounts of product (hat were usually 
obtained m nuclear processes It was 
fortunate, therefore, that a notable dis- 
covery made it possible to identify, 
in many cases, the products of nuclear 
transmutations even when they were 
obtained m amounts which, if sep- 
arated, would not have been visible 
under a microscope 
10 78 In the course of a study of 
the effect of alpha particles, from the 
naturally occumng radioelement polo- 


nium, on the nuclei of certain hght 
elements, boron, magnesium and alumi 
num, m particular, I Joliot-Cune and 
her husband, F Johot, to whose work 
reference was made in Chapter II 
(§1 2 75, 2 111), found that, m addi 
tion to protons, there was an emission 
of neutrons and positrons (positive 
electrons) This result was not at all 
extraordinary, since the nuclear process 
appeared to be essentially of the (a,p) 
type discovered by Rutherford, and a 
neutron and a positron could together 
be regarded as the equivalent of a 
proton But, early m 1934, the mii- 
pnsmg fact was noted that, although 
the formation of protons and neutrons 
ceased when the source of alpha parti- 
cles was removed, the positrons con- 
tmued to be emitted Reporting on 
(heir resuJts, JohoC-Cune and Johot 
wrote “Our latest experiments have 
shown a very stnkmg fact, when an 
aluminum foil is irradiated [with 
alpha particles], the emission of poa- 
trona does not cease immediately when 
[the source of the alpha particles] 
is removed The foil remains radio* 


* Values down to 10~** sq cm per nucleus have been measured, but smaller values imdoubt- 
edly occur , 

t The terra "bam’ was proposed in 1942 by the American physicists M G Holloway aiw 
C P Baker, as the result of a broadly humorous association of idea® It served the 
of a code word, which was desirable at the tune and seemed appropriate because a cr^ 
section of 10^* sq cm for nuclear processes wiw really as bie as a bam ’ (Los Alamos Report, 
LAMS 523) 3 ^ 


Nndjcar Trammuialion and Artificial Radioacimhj 


active nnd the emission, of radiation 
decays exponentially as for an ordinarj’’ 
fnaturally occurring] radioclcment. 
obscr^'cd the same phenomenon r\dth 
boron and magnesium. . . . The trans- 
mtitation of boron, magnesium and 
aluminum by alpha particles has given 
birth to nevr radioelcmcnts emitting 
po.sitrons. . , . It i.s probable that . . . 
[thc.«e species] are unknoum isotopes 
which are always unstable." 

10.79. According to the Joliois, the 
nuclear process was actually of the 
(a,n) t,vpc, so that in the interaction 
of alpha particles with aluminum, for 
example, the reaction occurring was 

,sAF + -He* + onb 

The P” isotope of phosphorus obtained 
in thi-s m.'uuicr, which is not found in 
nature, would then be the radioactive 
species which decayed with the emis- 
sion of a positron; the latter is repre- 
f'cnted hy the sjunbol +ic", since it 
has a single positive charge but a wtu- 
ally r.cro mass, and so the decay process 
would ho 

isP*"' +1^'’ -f i<Si”, 

the final product being Si^^, a .stable, 
naturally occurring isotope of silicon. 

10.80. In order to confirm this sug- 
mcchani'^rn, aluminum foil was 

O-Kpo^cd to alpha particle.s, .and then 
dissolved in hydrochloric acid solu- 
tion. Tlio hydrogen gas evoh'cd was 
found to carrj- with it the positron 
emitting activity, presumably in the 
form of pho'^nbine (PIIA containing 
ih*'- radio-active phosphpni.*;. Further, 
when the irKidiatcd .aluminum was dis- 
salvctl in a mixture of hydrochloric .and 
nitric acids, a small quantity of sodium 
pho-ph.ate added tis carrier (§5.29), 
.and then .a rircouium .*:alt. the }Wcipb 
t.ate of cireunium phosphate carried 


with it the radioactivity. The unstable 
species, which gives off positrons, thus 
appears wherever phosphorus, in the 
form of the appropriate compound, is 
to be expected. It is thus reasonably 
certain that the reaction of alpha parti- 
cles on aluminum is of the (a,n) type, 
the product being an unstable isotope 
of phosphorus, decaj^ing at a measur- 
able rate. Similar transmutations oc- 
cur with boron and magnesium, the 
products being radioactive nitrogen 
(N”) and silicon (Si”), respectively. 

10.81. "Vt^ien the phenomenon of ar- 
tificial radioactivity, as it is called, was 
first discovered, Joliot-Curie and Joliot 
suggested distinguishing the unstable 
isotopes by the use of the prefix radio, 
noth the name of the corresponding 
element; for example, radiophosphorus, 
radionitrogen and radiosilicon. But 
this nomenclature, although still in use 
to some extent, htxs proved inadequate 
because many elements exist in several 
different radioactive forms. It is con- 
sequently the present practice to iden- 
tify a radionuclide by giving its half 
life period (§ 5.46) and its inass num- 
ber, in addition to its name or sj’’mbol. 
Uius, the radionitrogen obtained by 
the interaction of alpha particles with 
boron would be described as 9.93-min. 
N*®, since its half life is 9.93 minutes 
and its mass number is 13. It may be 
mentioned in this connection that the 
Joliots found the radioactixdty of the 
substances obtained by nuclear bom- 
bardment to decay in an exponential 
manner, just as for the naturally oc- 
curring radioelements. It is thus pos- 
sible to assign a half life to each 
si>ecics, and these liave the general 
significance described in Cliapter V. 

10.82. In addition to bringing to 
light the existence of radioactive iso- 
topes, commonly referred to as radio- 
■isofopes, of normally stable elements, 
the work described above was impor- 



266 


SouTc^ool. on AUmic Energy Chap X 

tant for another reason Asitsauthora number43and61,whichaienotknown 
pointed out “These experiments give to occur in nature — at least not with 
the first chemical proof of artificial any degree of certainty— have been 
transmutation, and also proof of the isolated in radioactive forms Six ele- 
capture of the alpha particle in these ments beyond uranium m the periodic 
reactions ” Evidence for nuclear reac- system, which may have once existed 
tions had previously been based largely m nature but have now decayed al 
on cloud-track photographs, and the most completely, have been prepared, 
nature of the product had to be m- one of them, plutonium, in relatively 
ferred When the latter is radioactive, large quantities The major portion 
however, it can be identified posi- of this work has been, earned out m 
tively, and the mechanism of the proc- the United States, and represents a 
ess can be definitely established Al- remarkable achievement (see Chap 
though the product is obtained m ter XV) 
infinitesimal amounts, its path m 

chemical reactions can be followed by Identification of Radioisotopes 
its radioactivity Since it is an isotope 10 B4 When one or more radioac- 
of a familiar element, and hence has tive nuclides have been produced as a 
chemical properties which are virtu- result of a transmutation reaction, it 
ally identical with the knowm prop- is necessary to identify the element 
erties of this element, its identification with which each is isotopic, and then 
is a relatively simple matter An indi- to assign to it its proper mass number 
cation of the procedure m the case of If several active substances are formed 
radiophosphorus was recorded above, as in fission and spallation processes, a 
and other instances will be given later partial or complete separation is neces- 
10 83 The announcement of the for- sary In any event, it is frequently 
mation of artificial radioisotopes of desirable to separate a product from 
normally stable elements of low atomic the target element in order to obtain 
number as the products of alpha-par- material of higher specific activity, that 
tide bombardment naturally aroused is, with a greater activity per unit mass 
considerable mterest among physicists (§ 16 36) The methods of separation, 
m all parts of the world In addition which are quite similar to those em- 
to confirming the results reported by ployed for the natural radioelements 
the French scientists, it was soon found (§ 5 29), ivill be referred to again later 
by Dtber^ ns ihe- Johois^ hsd prpsheied, jto rfuinecJjoD watb the identification of 
that radioactive isotopes were formed theproductsof nuclearfission (§ 13 75) 
mmanynuclearreactions * Sincel934, For the present, all that is necessary 
a total of more than seven hundred is to suppose that the active ma- 
different radioactive isotopes of all the tenal to be studied is available m a 
known elements from hydrogen to form m which the radioactivity is defi 
uranium, have been obtained as a re- nite enough to be measurable, and that 
suit of a variety of transmutation proc- if more than one substance is present, 
esses, includmg fission and spallation the half lives are such that each can 
. In addition, the elements of atomic be distinguished from the other Hiese 
} ‘In 1933, before the discovery of artificial radioactivity, W D Harkms D M Gans 
/ H W Newson, m the United States had SQggested that the transmutation of fluorine by 
neutrons occurred by the P*(na)N” proce^ and that the product N“ might decay to tne 
stable O’* by the emission of a beta particle Tnis prediction was later confirmed N’* is raoJ^ 
active and emits beta particles 



267 


7\vcUar Transtnulatmt and Artificial Radioaclh'ify 


requiromenls arc not too exacting, and ! 
are nsnally met without difficulty, cx- j 
ccpt when fission and spallation prod- ! 
nets are involved. 

10.86. Having secured the material 
in suitable form, the next step is to 
study the rate of decaj’-, so that the 
))articular specie.^, characterized b 3 ' its 
half life, may be chosen. For this 
purpose a form of Geiger-MOlIer radia- 
tion counter, described in Chapter VI, 
is frequently used. High-speed pos- 
itrons, such as are expelled from ar- 
tificially radioactive nuclei, produce 
ionization in their path, just as do 
electrons, so that thej- can be counted 
in the same manner. Since most artifi- 
cial radionuclides have half lives which 
are neither extremely short nor exces- 
sively long, thej' can generally be eval- 
uated by plotting the logarithm of 
the counting rate, determined after 
various intervals of time, against the 
time, iis indicated in § 5.51 and illus- 
trated in Fig. 5.3. If the substance 
under examination contains two or more 
active species, each can be identified 
by its half life, iirovided the values are 
sufficiently difTerent. 

10.8G. Since the half life is a definite 
propert3' of a particular nuclide which 
is independent of its phj^sical condition 
or of its state of combination, it pro- 
vide.s h simple and idrlually infallible 
means for keeping track of the given 
.Species through a .series of physical 
and chemical processes. Because G-M 
counters and other simihar devices c.an 
count individual particles emitted b^-^ 
radioactive elements, the latter can bo 
detected in amounts as small a-s 10"'- 
gram, or lc.ss (§ JG.35). Such amounts 
are, of course, far beyond the reach .of 
onlinarv* conventional analj'tical pro- 
WKlures. 

10.87. In order to determine the par- 
ticular clement with which the active 


species is isotopic, the experimental 
material is dissolved in a suitable man- 
ner, and stable compounds of two or 
three suspected elements are added to 
the solution. One or other of these 
elements should be isotopic ivith the 
radioactive substance, and hence should 
act as a carrier (§ 5.29) for it, since 
their properties aviU be identical. Fa- 
miliar chemical and physical methods 
of separating the elements are then 
applied, and the bchaxdor of the active 
material can be readily traced by de- 
termining the radioactivity of various 
parts of the system during the course 
of separation. 

10.88. The procedure may be illus- 
trated bj' means of a simple example.* 
A sheet of iron was bombarded with 
5.5-Mev deuterons, when it was ob- 
served to develop a beta-particle activ- 
ity v-ith a half life of 47 days. The 
active species might possibly be iso- 
topic with the target material, iron, 
if the tran-smutation process were of 
the id,p) tjqjc, or it might be a form 
of mang.anese, resulting from a (d,a) 
process, or of cobalt, if the nuclear 
reaction wore of the ((f,n) type. Hence, 
after exposure to deuterons, the iron 
sheet was dissolved in hydrochloric 
acid and oxidized to the ferric state 
bj' means of nitric acid. Small amounts 
of manganous and cobalt chlorides were 
then added so tliat the solution con- 
tained manganese, iron and cobalt, and 
it was necessarj' to find with which of 
these elements the 47-daj’' activity 
v,'ould be associated when separated 
from the others. Tlie solution was 
made ON with respect to hj^drochloric 
acid and then extracted with ether, 
which is able to di.ssolve the ferric 
chloride, hut not the cldorides of co- 
balt and manganese. The actixity was 
found to pass into the ether solution, 
indicating that the radioactive species 


fit" 


n. Mmrwnat dilTm'n*. is dt'scril^d in § 10.1 IS. 



268 Sovr^hook on 

as isotopic with iron After extractr- 
mg the solution several times with 
hydrochloric acid, to remove all traces 
of manganese and cobalt, the feme 
chlonde was converted into solid fer- 
ric oxide and the half life of the activ- 
ity determmed It was found to be 
47 days, as m the original material 
after bombardment, and so the actne 
product nas in all probability an iso- 
tope of iron 

10 89. Now the element has been 
identified, it is necessary to consider 
the more difficult task of determining 
Its mass number When appreciable 
quantities of matenal are available, 
as has been the case mth the sloa- 
neutron fission products of uranium- 
235, mass-spectrographic methods can 
be used successfully to yield unequiv- , 
ocal results In other instances, hon- , 
ever, indirect procedures must be | 
adopted The so-called cross bombard- 
ment method generally employed is to 
try to obtain the particular species 
by a number of different nuclear reac- 
tions, from the results it is often pos- 
sible to infer the mass number of the 
actue nuclide For example, in order 
to assign a mass number to the 47-day 
isotope of iron, cobalt oxide was ex- 
posed to the action of neutrons of 
moderate energy, when it was ob- 
served that a 47 -day beta activity de- 
veloped Upon dissolving the resulting 
matenal in hydrochlonc acid and add- 
ing feme and manganous chlondea, 
it was found that the activity could 
be extracted together with the f^mc 
chloride by means of ether, as de- 
senbed above It is evident, therefore, 
that deuteron bombardment of a stable 
isotope of iron, and neutron bombard- 
ment of a stable isotope of cobalt, pro- 
duce the same radioisotope of inm 

10 90. The process occumng m the 
former case must be of the (d,p) type, 


Atomic Energij Chap X 

as stated above, since the atomic num- 
ber remains unchanged, and so it fol- 
lows that the mass number of the 
product must exceed that of the target 
nucleus by unity The stable isotopes 
of iron have mass nnmbcrs of 54, 56, 
67 and 58, and hence the respective 
products of the (d,p) reaction would 
have masses of 55, 57, 58 and 59 Smee 
the mass numbers 57 and 58 are those 
of stable isotopes of iron, it follows 
tliat the imstable 47-day radioironmust 
have a mass number of either 55 or 59 
10.91. A choice between these values 
may be made by considenng the neu- 
tron reaction with cobalt m which the 
same isotope of iron is obtained This 
reaction must be either (n,p) or (n,d), 
since the atomic number of the product 
(iron) 13 one unit less than that of the 
target element (cobalt) However, the 
(n,d) reaction is improbable, since tbs 
requires neutrons of very high en- 
ergy, and hence it must be concluded 
that the process under consideration 
IS Co(n,p)Fe, the product must then 
have the same mass number as the 
transmuted isotope of cobalt The 
stable isotopes of the latter have mass 
numbers of 57 and 59, and so the mass 
of the radioiron formed must be 57 
or 59 Since the value, as seen above, 
IS either 55 or 59, it is at once evident 
that the correct mass number is 59 
The radioactive isotope of iron, with 
a half life of 47 days, is thus to be 
represented by the symbol Fe®® 

10 92 The foregoing example may 
be taken as more or less typical of the 
general cross bombardment procedure 
adopted for the assignment of mass 
numbers IVhen the particular radio- 
isotope can be obtained m several dif- 
ferent ways, the problem is simplified, 
but a decision may be more difficult 
when the target elements have many 
isotopes 



269 


'Nuclear Transniutalion and Ariifitdal Radioaclivdy 


Decat or Abitficial Radioisotopes 

10.93. The first artificial radioiso- 
topes to be identified decayed by the 
emission of positrons (§ 10.76), but 
later investigations showed that other 
types of decay were even more com- 
mon. Tlic emission of alpha particles 
has hitherto been detected for a few 
elements with atomic numbers less than 
83, as will be indicated shortly. On the 
other hand, beta acti\*ity, accompanied 
by the emission of (negative) electrons, 
has been observ’ed wdth the majority of 
artificial radionuclides. Prior to the 
year 1917, the knowm positron-emitting 
species were restricted to elements of 
moderately low atomic number, but 
nuclear transmutation by spallation 
has led to the isolation of several such 
radioi-sotopcs of f airlj’’ liigh atomic num- 
1x:r, and more arc to be expected. In 
afldition to decay by the emission of 
electrons and positrons, other tj-pcs of 
radioactive change, which will be de- 
scribed below, have been obsenmd. 

10.94, It will be seen in Chapter XII 
that among the more than two hun- 
dred .and seventy stable nuclides, e.xist- 
ing in nature, the ratio of neutrons to 
protons in the nucleus falls within 
a somewhat limited range, which 
varies with the atomic number. If 
in a particular species the neutron-to- 
prolon ratio is larger than the stabil- 
ity range, the isotope will be unstable, 
llic latter could acquire stability, or 
at ie.^st liecome more stable, if a neu- 
tron were replaced by a proton, thus 
decreasing the ratio of neutrons to 


protons. As can be seen from equation 
(”•12). this is precisely what happens 
when a nucleus expcl.s a negative elec- 
tron, that i,s, a beta particle. Hence 
nuclei containing too many neutrons 
for ftabdity are negative beta-active, 
5uch species have m.'Uvs numbem whid: 
r-Tf? larger llian those of tlic atabh 


isotopes; for example, O'®, 

Al^, CP®, Fe® and Br®®. These nu- 
clides are often obtained in {d,p), {n,p), 
{n,a), (n, 7 ) and (t,p) processes, since 
the product in each case has a larger 
ratio of neutrons to protons than does 
the target element. 

10.95. Tilien the neutron-to-proton 
ratio of a nuclide lies below the range 
for stable existence, this neidron-deji- 
cient nucleus will tend to change in 
such a manner as to replace a proton 
by a neutron. There are three ways 
in which this can occur: one is the 
emission of a positron, the second is 
the expulsion of an alpha particle, and 
the third is the capture of an orbital 
electron (§ 10.109). Positron actuity 
is commonly observed with isotopes 
having mass numbers smaller than the 
stable values. Examples of this type 
arc C”, N>®, 0“, Al®®, CP®, Fe®® and 
Br®®, which may be compared wdth the 
electron-emitting isotopes of the same 
respective elements ^ven above. Nu- 
clear reactions of the {p,n), {d,n), {a,n), 
(71, 2n), (r,7i) and (t,27i) tjqjes result 
in a decrease in the relative propor- 
tion of neutrons, so that the products 
are frequently positron active. 

10.96. In high-energy, spallation re- 
actions, it frequently happens that the 
nucleons which split off first are neu- 
trons, lea\ing neutron-deficient nuclei 
irith atomic numbers not very differ- 
ent from those of the target element. 
Such nuclei are radioactive and decay, 
as is to be expected, by the emission 
of positrons, 

10.97. In a few instances, of which 
Cu*^ is a notable example, discovered 
by C. C. Van Voorhis in the United 
States in 1936, radioactive decay oc- 
curs w'ith the emission of both posi- 
trons and negative electrons. This is a 
typo of branched disintegration (§ 5.60) 
in which some nuclei decay in one 



268 Sourcebook on 

as isotopic ■with iron After extract- 
ing the solution several times ivith 
hydrochloric acid, to remove all traces 
of mang'inese and cobalt, the fernc 
chloride was converted into solid fer- 
ric oxide and the half life of the activ- 
ity determined It was found to be 
47 days, as m the original matenal 
after bombardment, and so the active 
product was in all probability an iso- 
tope of iron 

10 89. Now the element has been ' 
identified, it is necessary to consider ' 
the more difficult task of determining ' 
its mass number When appreciable ' 
quantities of material are available, ' 
as has been the case with the slow- I 
neutron fission products of uranium- 
235, mass-spectrographic methods can 
be used successfully to yield unequiv- 
ocal results la other instances, how- 
ever, indirect procedures must be 
adopted The so-called cross bombard^ 
merit method generally employed is to 
try to obtain the particular species 
by a number of different nuclear reac- 
tions, from the results it is often pos- 
sible to infer the mass number of the 
active nuclide Tor example, m order 
to assign a mass number to the 47-day 
isotope of iron, cobalt oxide was ex- 
posed to the action of neutrons of 
moderate energy, when it was ob- 
sen ed that a 47-day beta actu ity de- 
veloped Upon dissolving the resulting 
matenal m hydrochlono acid and add- 
ing ferric and manganous chlondcs, 
it was found that the activity could 
be extracted together with the feme 
chlonde by means of ether, as de- 
scribed above It is evident, therefore, 
that deuteron bombardment of a stable 
isotope of iron and neutron bombard- 
ment of a stable isotope of cobalt, pro- 
duce the same radioisotope of iron 

10 90 The process occumng m the 
former case must be of the (d,p) type, 


Atomic Energy Chap X 

as stated above, since the atomic num 
ber remains unchanged, and so it fd 
lows that the mass number of the 
product must exceed that of the target 
nucleus by unity The stable isotopes 
of iron have mass numbers of 54, 56 
57 and 58, and hence the respectue 
products of the (d,p) reaction would 
have masses of 55, 57, 58 and 59 Since 
the mass numbers 57 and 58 are those 
of stable isotopes of iron, it follows 
that the unstable 47-day radioironmmt 
have a mass number of either 55 or 59 
10 91. A choice between these values 
may be made by considering the neu 
tron reaction with cobalt m which the 
same isotope of iron is obtained This 
reaction must be either (n,p) or (»,d), 
since the atomic number of the pr^uct 
(iron) 13 one unit less than that of the 
target element (cobalt) However, the 
(n,d) reaction is improbable, since this 
requires neutrons of very high en 
ergy, and hence it must be concluded 
that the process under consideration 
IS Co(n,p)Fe, the product must then 
have the same mass number as the 
transmuted isotope of cobalt The 
stable isotopes of the latter have mass 
numbers of 57 and 59, and so the mass 
of the radioiron formed must be 57 
or 59 Since the value, as seen above, 

13 either 55 or 59, it is at once evident 
that the correct mass number is 59 
The radioactive isotope of iron, with 
a half life of 47 days, is thus to be 
represented by the symbol Fe* 

10 92 The foregoing example may 
be taken ns more or less typical of the 
general cross bombardment procedure 
adopted for the assignment of mass 
numbers When the particular radio- 
isotope can be obtained in several dif- 
ferent ways, the problem is simplified 
but a decision may be more difficult 
when the target elements have many ) 
isotopes 2 



271 


Nvckar Tra7wmtialion and Artificial Radioactivity 


vrhorc Ga’* is a knovra stable isotope 
of ptaHiura. 

10.101. For reasons which w’ill be 
made clear in Chapter XIII, the prod- 
ucts of nuclear fission usually contain 
s'cveral more neutrons than is permis- 
sible for stability. These substances 
consequent h’- decay by the emission 
of nepative beta-particles (/5“), and 
severfil chains of four or five disintegra- 


proton — > neutron 
IMa-Ss 1 1 

Charge 0 


tion stages have been observed; one 
instance is the scries 

:,Kr» £; jrRb” £, ssSr^^ ££ fl, 

the end product, being the most 
abundant stable isotope of zirconium, 

Posmve AKD NEGATn'E 
Beta Activity 

10.102. Becnusc the 'characteristic 
featurc-s of positive and negative elec- 
tron emission are so much alike they 
are both classified as beta activity, 
with llic appropriate qualification of 
positive or negative, respectively. Fur- 
ther, the general behavior is essen- 
tially the same as that observed with 
natunrily occurring radioactive ele- 
ments which dee^y by the emission 
of a l>eta particle. Tlie discussion of 
k>ta activity given in Chapter YII 
m.Hy tljus bo regarded as applying 
i-qually to natuml and .artificial radio- 
nudidf'o. 

10.103, For .all po-^itron .and electron 
eauttors that have been studied, the 
particles exhibit a continuous distribu- 
t =''•?! of cnerg:.-, as described in § 7.4S 
aim illudrated in Fig. 7,7. The neu- 


trino- theory of beta dec.ay (§ 7.49), 
according to wliich an electron is pro- 
duced in a radio.active nucleus by the 
conversion of a neutron into a proton, 
an electron and a neutrino, appears to 
apply also to artificial radioelemenls. 

10.104, Since atomic nuclei do not 
contain positrons, it is supposed that 
prior to its emission a positron is (tre- 
ated in the nucleus by a process 
analogous to that represented by equa- 
tion (7.12), namely, 

-b positron antineutrino (10..3) 

0 0 

+ 0 

The simultaneous formation of an en- 
ergj'-cnnying particle, called an anii- 
nentrino, is postulated to account for 
the energy distribution among the pos- 
itrons. Although the hypothetical par- 
ticle is referred to here as an antineu- 
trino, there is nothing, as far as is 
known, to distinguish it from the neu- 
trino accompanying the conversion of 
a neutron into a proton. The general 
neutrino theory, as developed by Fermi, 
should thus apply to positron emission, 
and Kurie (or Fermi) plots of equation 
(7.13) arc actually found to be straight 
lines, as required by the theoryx Devia- 
tions .arc, however, observed at low 
energies just as for negative beta- 
decay. 

10.106. The maximum energies of 
positrons and electrons from artificial 
mdioclements are related to their re- 
.'pective m.aximum range,s in a manner 
exactly similar to Oiat described in 
^7.62, and equation' (7.14) may be 
used to calculate if the range 
has been detemiined from absorp- 
tion measuremenis. Further, by the 
neutrino tlieory the maximum energy' 
should be related to the radioacti\*e 
decay constant X by the Fermi equa- 



270 Sourcebook on Atomic Energy Ckap X 


manner and some in the alternative 
manner, the half life being the same m 
each case It is of interest to note 
that the mass numbers of the stable 
copper isotopes are 63 md 65, so 
that Cu“ has a neutron to proton ra- 
tio which lies between the values for 
the two stable species 

10 98 It was seen in Chapter VIII 
that when a radioelement emits a neg- 
ative beta particle, the product has 
the same mass number as the parent, 
but its atomic number is greater by 
one unit This rule applies, of course, 
to any radioactive nuclide, natural or 
artificial When a positron is emitted 
the mass number is still unchanged, 
but the atomic number of the product 
is now one unit less than that of the 
parent This conclusion follows im- 
mediatelj from the postulate made 
above and v\hich will soon be con- 
sidered more fully that positron emis- 
sion IS associated m ith the replacement 
of a proton by a neutron This change 
clearly leaves the total mass unaffected, 
but decreases the number of protons, 
and hence the nuclear charge and the 
atomic number, by unity The same 
conclusion is reached by balancing the 
mass numbers and atomic numbers, as 
IS the general practice in equations for 
nuclear reactions Tims, considering 
the two modes of decay of copper-64, 
the equations are 

mCum + aoZn«, 

where +ie° and represent a positron 
and an electron, respectively The 
products are stable isotopes of nickel 
and zmc, both of which are found in 
nature 

10 99 Until recently, the only known 
alpha emitters apart from a naturally 
occumng samarium isotope, were nu- 
clides of atomic number 83 or more 


In September 1949, S G Thompson 
A Ghiorso, J 0 Rasmussen and G T 
Seaborg of Berkeley issued a prelim 
inary report of the discovery of alpha- 
active isotopes of gold and mercury 
(atomic numbers 79 and SO), and, much 
more significantly, of certain rare earth 
elements, with atomic numbers m the 
region of 65 to 67 and mass numbers 
of about 150 By bombarding the ox 
ides of samarium, gadohnium and dys- 
prosium w ith 200-Mev protons, several 
alpha-particle activities, possibly due 
to isotopes of gadolinium, terbium 
holmmm or dysprosium, were detected 
Tlie capture of the high energy proton 
IS probably accompamed by the emis- 
sion of several neutrons, leaving neu 
tron-deficient nuclei, such as «sTb’“ 
and a possible reason why 

these nuclides decay by the emission 
of alpha particles, as well as m all 
probability, by positron emission or 
electron capture, will be indicated in 
§ J2 34 There is no doubt that as the 
fundamental principles become appar 
ent, other alpha active nuclides of me- 
dium mass number will be discovered 
10.100 With the majority of, al 
though not with all, artificial radionu 
clid^, other than those obtained by 
nuclear fission and spallation, the im- 
mediate decay product is a stable spe- 
cies, as in the two reactions considered 
above The result is not surprising 
if it 13 recalled that the radioisotopes 
are usually obtained by a simple trans- 
mutation in which a particle enters a 
stable nucleus and another particle is 
expelled In spallation, however, the 
splitting off of several nucleons, as 
indicated earlier, may leave a product 
that IS two or three, or po^iblj more, 
stages removed from stability Short 
chains, involving two or three succes* 
sive positron emissions, are then pos- 
sible before a stable nuclide is reachw, 
tiius, representing the positron by F * 



273 


Nuclear Transmutation and Artificial Radioacliaity 


wtli, and be annihilated by, electrons 
(§2.77). The enerp^ of the annihila- 
tion radiation is in , the gamma-ray 
range, but it is to be regarded as sec- 
ondarj', and not directly connected 
v.'ith the radioactive decay process, 

0RnrrAi/-Ei.i:cTRON Capture 

10,109. In some instance.s, where the 
ratio of neutrons to protons is low, 
and hence positron activity would be 
expected, another type of decaj’’ has 
l)cen found to occur with artificial 
nuclides. Instead of a proton being 
converted into a neutron with the 
emission of a positron, the nucleus cap- 
tures one of the extranuclear (orbital) 
electrons, which immediately combines 
with a proton to form a neutron; thus, 

proton -f electron 
iMass 1 0 

Charge +1 —1 


10.110. The phenomenon described 
above is referred to as decay by or- 
biial-clcclron capture. The electron is 
usually captured from the first quan- 
tum level, i.e., the K level (§ 4.72), for 
such an electron is more likely than 
any other to be found near the nucleus; 
consequently, the expression K-eleclron 
capture or, in brief, K-capture is often 
employed. Instances of an electron 
being captured from the L level are 
known, although they are not com- 
mon, The possibility of orbital-electron 
capture as an alternative to positron 
emission w’as predicted the Japanese 
mathematical physicists H. Yukawa 
and S. Sakata in 1936, and proof of its 
reality was obtained in the United 
States by L. W, Alvarez in 1938. 

■ -♦ neutron -f neutrino (10.4) 
1 0 

0 0 


with n neutrino, or similar particle, 
In-ing formed at the same time.* It 
will be seen that this process provides 
an alteniativc to that represented by 
equation (10.3) for the replacement of 
a proton by a neutron, thus increasing 
the noutron-to-proton ratio. The prod- 
uct of this tjq)e of radioactivity' would 
h.svo the same mass number as its 
parent, but its atomic number would 
1 m? one unit lower, j\ist as in the case 
of positron emission. TIic decay of .an 
unstable species, such as Fe”, by or- 
bital electron capture, can be repre- 
Ktitcd by the equation 

-f :5hln«, 

tl'.e electron which is captured by the 
imn nucleus Wing indicated by _if^ on 
th" Icft-liand side. 


10.111. The detection of orbital-elec- 
tron capture depends on the fact that 
the removal of the extranuclear elec- 
tron leaves a vacancy in the appropri- 
ate quantum level, usually' the lowest 
or K level. .(In electron from one of 
the liighcr energy' levels vdll then im- 
mediately move in to fill the vacant 
position, and the excess energy will be 
emitted as the corresponding charac- 
teristic X-ray, as described in § 4,72. 
Since the orbital-electron capture must 
precede the electronic transition and 
the emission of X-rays, the latter will 
be characteristic of the product nucleus 
with an atomic number one imit less 
than that of the radioactive species. 
A case in point is the 600-dny vana- 
dium isotope of m.ass number 49; the 
decay of this nuclide was found to 
! be accompanied by the characteristic 


«'^”'4vU|5-ctron a definite energy' the neutrino, or its equivalent in this case. 

energies as in positron or 



274 Sourcebook on Atonnc Energy Chap X 


X-rays of the K senes belonging to 
the element titamum which precedes 
it in the penodic system The mten- 
sity of the X-rays falls off as the active 
matenal decays It is evident, thwe- 
fore, that decays by X-electron 
capture 

10 112 If, as a result of orbital- 
electron capture, the product nucleus 
is left m its ground state, the change 
^vlU not be accompanied by gamma 
rays, such behavior, of which the 600- 
day V*® provides an example, is re- 
ferred to as pure K-capture In most 
instances, however the product nucleus 
IS formed in a high energy (excited) 
state and the excess energy is gi\en 
off m the form of gamma radiation 
Quite frequently, too, this radiation 
IS internally con\erted (§7 85), that 
IS to say, the energy of the gamma- 
ray photon IS transferred to an orbital 
electron vhich is consequent!} ejected 
The result is a “line” spectrum of 
electrons of definite energy, associated 
with X-rays characteristic of the prod- 
uct element The latter would, of 
course, be indistinguishable from those 
due directly to orbital-electron capture 

10 113 It w ill be shoiv n presently 
that certain energy conditions are nec- 
essary for positron emission to be pos- 
sible Since orbital-electron capture 
leads to the same disintegration prod- 
uct, this process of decay may occur 
simultaneously wnth the positron ac- 
tivity If the energy requirements are 
not met, how ever, orbital-electron cap- 
ture takes place exclusively, with or 
■without accompanymg gamma radia- 
tion Suppose that in a particular 
nuclide the ratio of neutrons to pro- 
tons IS smaller than the value needed 
for stability, so that positron emission 
IS conceivable If the nucleus ejects 
a positron, its mass will decrease by 
mo, where mo is the rest mass of the 
electron, which is the same as that of 


a positron, the mass of the accompany 
mg neutrino is neglected since it is so 
minute Further, since the atomic num- 
ber of the product is smaller by one 
unit than that of the parent radionu 
chde, the former •wiH have one orbital 
electron less than the latter, this mil 
also represent an additional decrease 
of wto m the mass of the atom as a 
whole It follows, therefore, that, when 
positron emission takes place, the iso- 
topic mass of the product must be 
smaller by the amount 2mo than that 
of the positive beta-active parent 
10 114 Actually this is a TnimmnTn 
value, for the mass diSerence may be 
larger than 2}no, but it cannot be less, 
if positron decay is to be possible 
Thus, if il/(A) represents the isotopic 
weight of the parent element A and 
Af(B) that of the product B, the con- 
dition for positron emission is 

^fCA) - MiB) > 2mo 

Tlie rest mass of the electron is 0 00055 
on the atomic weight scale, hence for 
positron emission to be possible the 
isotopic iveighfc of the parent must 
exce^ that of the product by 0 0011, 
at least Since the mass difference 
eventually appears as energy, the quan- 
tity 2mo, 1 e , twee the rest mass of 
the electron, may be replaced by its 
energy equivalent, this was showm in 
§ 3 81 to be 1 02 Mev, so that the 
condition becomes 

(A) - > 1 02 Mev 

It IS seen, theiefore, that for positron 
activity to be possible at least 1 02 Mev 
of eneigy must be available, as a re- 
sult of the loss m mass associated with 
the change fiom nuclide A to nuclide 
B Energy in excess of this mmimuin 
will be shared between the ejected 
positron and the accompanying neu- 



275 


Nvclear Transmidation and Artificial Radioactivity 


irino, althougli some may appear as 
gamma radiation. 

10.116. WTien the mass difference 
Mik) — ii/(B) is such that the mini- 
mum of 1.02 Mev of energy is not 
available, then the change from A to B 
wll occur by orbital-electron capture, 
assuming as before that the neutron- 
to-prolon ratio in the parent nucleus 
is smaller than requisite for stabilitju 
For this alternative process the energy 
demand is much less stringent. In- 
stead of the positron being ejected 
from the nucleus while at the same 
time an orbital electron is expelled, 
as explained above, the same change 
from A to B is now achieved by the 
orbital electron going into the nu- 
cleus. The minimimi mass difference 
jlf(A) — M(B) is now equal to the 
mass of the neutrino, which is virtu- 
ally jcro; hence, the only requirement 
for decay by orbital-electron capture 
i? that ili(B) should be loss than il/(A), 
the actual difference being of no conse- 
quence. Any energj' that is available 
due to the isotopic weight of the prod- 
uct being appreciably less than that 
of the parent uill appear us gamma 
radi.ntion, apart from some which may 
be (’.'uried off by the neutrino in equa- 
tion (lO.'l).* 

lO.llG. \Vlicn competition between 
decay by electron capture and by posi- 
tron emi&rion is possible, the former 
prot'e*^s is favored by factors which 
inerea.'T' the h.alf life of the parent 
flcmcnt. In view of the relatiomship 
iH’tween the half life and the maximum 
of the positrons (§ 10.10-1) it 
ran be STen that the extent of electron 


capture uill increase as’ the energv’^ 
decreases. In other words, astheenergj’- 
of the radioactive change approaches 
the minimum value of 1.02 Mev, the 
probability of decay by positron emis- 
sion decreases wliile that of electron 
capture increases. Wlien the energj’’ 
is less than 1.02 Mev, the latter process 
occurs exclusively. Two other factors 
tend to favor orbital-electron capture 
relative to positron emission: one is 
high atomic number and the other is 
a large difference in the nuclear-spin 
quantum numbers of the parent and 
product nuclei. Positron emission is 
verj’’ rare among the hea\dest elements, 
although several cases of JT-capture 
have been recorded. 

Nuclear Isomerism 

10.117. Another tjqie of radioactive 
decay, i.e., by isomeric transition, has 
been brought to light by a study of 
art ificial radionuclides, although it is ac- 
tually an aspect of the familiar gamma- 
ray emission. The possibility that there 
might exist nuclides luiving the same 
mass number and also the same atomic 
number, that is to say, isoharic iso- 
topes, but possessing different radio- 
active properties was envisioned by 
F. Soddy in 1917. Substances of this 
tvqie have now become loiown as nu- 
clear isomers, based on the suggestion 
made by (Frl.) L. Meitner in 1936, 
and the phenomenon has been called mi- 
ckar isomm'sm .f Some four years later, 
the Gonn.an radioebemist, 0. Hahn, 
produced evidence for the existence 
in nature of a nuclide, which he called 
uranium Z, that appeared to be iso- 


f f pavirkcd hrw that in nepuivp ivtaHiccay, i.o., in electron emission, the mn.'^ 

necn-ases by esj, bnt there is .a corresponding increa'^o in the ma.'=s of the orbital 
'"f JwmlKr of which incrca.'cd by unity. There ere thus no cjicrgv restriction?, 
ti-e neutrino mass, and the ronditibiy ere .rimilar to th<x«e for orbitaf-elecLron cap- 
in f.acl of the negative-electron emission and the orbital<-!ectron 

tiering the revern' of each other, Init this is prokably not atricllv true. 
«turre, randli.ar v,-ith the tcm'.s ifomcr and Ao»ienVn,'’frpm the Greek rio 
AS appHt-d to compounds having identirs! compasitions and molecular 
' i... s'Ut dxtterjng in their pro{>erlic5. 


278 Sourcebook on Atomic Energy Chap y 

10 123. The second class consists of nuclei originally formed in the ground 
genetically related isomers, as repre- state, while the other group results 
sented in Fig 10 3, in which the meta- from the decay of nuclei in the same 
stable state decays to the ground state ground state produced by isomeric tran 
with a definite half life Ti, a gamma- sition from the metastable excited state 
ray photon being expelled This is the It is a well-known law that the over 
decay process knoAvn as isom me transt- all rate of any change taking place 
tion, abbreviated to I T In the major- m stages is equal to the rate of the 
ity of eases the gamma radiation is slowest of these stages, hence m the 
internally converted, so that what is process 

Metastable State Ground State Product, 

observed is a line spectrum of electrons, the rate of emission of the beta par 
together with characteristic X-rays, tides m the second group, although 
as IS usual ivith internal conversion they actually onginate from the ground 
(§ 7 86) * The ground state decays to state, appears equal to the rate of the 
form the product with a half hfe of isomenc transition, which is the slower 
Tj, which 13 different from Ti As stage 

before, the product is not necessardy 10.125. Isomenc transition is fre- 
formed m its ground state, so that quently accompanied by the breaking 
gamma radiation may accompany the of a chemical bond nhich may make 
radioactive change There is also a possible a separation of the isomenc 
possibility of some direct independent nuclei An interesting illustration is 
decay of the excited, metastable state provided by the isomers of tellunum 
of the parent, as indicated by the for example, Te'”, in the tabulation 
broken line Some instances of genet- given above If to a tellurate (Te'^) 
ically related isomers, which include solution, contammg this radioactive 
those of Br“, are the following species, is added some ordinary in 

So«(I T , 2 44 days, (J+-, 3 9 hr ) Br*>CI T , 4 4 hr , j?-, 18 mm ) 

Zn^d T , 13 8 hr , 57 nnn ) T , 48 days, /T, 72 sec ) 

Sc«(I T , 57 mm , 3", 19 mm ) Te«Hl T , 30 hr , p-, 25 mm ) 

10 124. It will be observed from the active tellurite (Te"), then upon sep- 

foregoing examples that the half life aratmg the latter chemically, it is found 

of the internal transition process is to contam the 25-mm isomer The 
often longer than that of the beta de- explanation of this behavior is that 
cay, positive or negative, of the ground the gamma ray ermtted by the upper 
state As a result, the radioactive sub- (30-hr ) isomenc state undergoes ifl 
stance emits two groups of beta parti- temal conversion, resultmg m the ejec 
cles, corresponding to two distinct half tion of an electron from a K or L 
hves One group, associated noth the level of the product atom, that is, from 
shorter half life, is due to decay of the lower (25-min ) isomenc state As 

• The X-rays are here those of the radioactive element itself, since this is the species enii^ 
tin§ the converted gamma radiation, and so isomenc transition can be distinguished from 
orbital-electron capture where the X-rays xe^tmg from internal conversion are those of ttie 
product element 



Nvclcnr Transimdalion and Artificial Radioaciiniy 


a result of what is known as (lie Auger 
effect, llic liigli energy' of this inner 
(k or L) electron is transferred to one 
or more of the outer (valence) elec- 
trons, which are consequently removed 
from the atom. Tlris detachment of 
valence electrons from the 25-min. iso- 
mer results in the brenlung of some of 
(ho bonds between the tellurium and 
oxygen atoms; consequently, the iso- 
meric transition is accompanied by a 







Fro. 10.3. Cicnctlcnlly rcl.atcd isomers: 
bornerie transition. 

change from the VI to the IV oxida- 
tion state, i.e., from tclluratc to lellu- 
rhe. Other genetically related isomers 
have been .separated chemically, and 
(hep'ncnd explanation of the behavior 
is analogous to that given licre for 
tellurium.* 

10.12G. The thial cailegorj' of nu- 
cle.ir isorncri-^m i.s that in wlijch the 
activi-* spicic.s aiv is.'aatrs of atahk nu- 
ch'i. The decay process now merely 
involves an isomeric transition from 
the ineta.stable excited slate to the 
imnind .'■tale of a stable nuclide, ac- 
curnsj.'snicd by the enii£*ion of gamma 
r.vbation. If this is intcmally can- 
’t < rO'd, there will bo a line spoctnim of 
!t ■. ron--, anti the clnamcteristic. X-ra\*s 


of the element will be emitted. About 
twenty stable species, which are found 
in nature, among them ICi-®®, Sr®^, Eh’“®, 
Ag**^, In”®, 00 ”° and Au‘®^, are Imown 
to form metastable states of appreci- 
able life, from a few seconds to several 
days. In addition, isomers with very' 
short lives, such as Ta*®' and Re'®’, 
wth half lives of the order of 10“® sec., 
have been reported and it is probable 
that many other stable nuclides will 
prove to have short-lived isomers. In 
order to distinguish the metastablc 
from the stable nucleus, it is the prac- 
tice to indicate the former by an as- 
terisk, for instance, Kr®®'^', as 

stated in § 10.25. 

10.127. Isomers of stable nuclides are 

frequently the result of nuclear excita- 
tion accompanying inelastic scattering 
of alpha particles, deuterons, protons 
or fast neutrons, as already de.scribcd 
in preceding sections. High-energy 
X-rays and electrons are able to pro- 
duce similar excitation, so that the 
products arc stable nuclides in meta- 
stable excited states of appreciable life. 
Isomers of stable species are also some- 
times formed in other nuclear proc- 
esses; examples are, Sr®®(n, 7 )Sr®'‘^, 
I'Cr®®(d,p)ICr®®*, Se®''*(a,7j)Ivr®®* and 

Cki“®(d,7z)In'”'^ In the first two cases, 
one stable isotope of an element is con- 
verted into the metastablc (isomeric) 
state of another stable isotope of the 
same element. As reported earlier, 
beta decay often leads to the forma- 
tion of the product in an excited state; 
this may bo a metastable state of a 
stable species, as is the case for the 
negative beta-decay of Br®® and Cd“®, 
the products being Kri®* and In”®*, 
respect ivoly. 

10.128. llie ex-planation gencrally 
i accepted for the existence of meta- 


Tfi.- r.' 










tvlnry" piwv.in th« .study of chcraicai rc.nr-tio.n'! rt.^uUinc from 
’ e; energy- pcMurt'-d in nurP^ir of various kinih 



280 


Soured)ook on Atormc Energy 


stable states, and hence of nuclear 
isomers, of both stable and unstable 
nuclides, is the one proposed by the 
German physicist 0 F von Weizsacker 
in 1936 If the energy difference be- 
tween the excited state and the ground 
state IS relatively small and, m addi- 
tion there is a considerable difference 
of angular momentum, that is, of re- 
sultant spin quantum numbers of the 


Chap X 

2 sm will then be observed There » 
insufficient information available coq 
cemmg nuclear spins to test this aspect 
of the theory but it is significant that 
the great majority of the known iso- 
meric nuclei contam odd numbers of 
nucleons, so that the nuclear spins are 
half integral and hence are liable to 
be large (§ 4 79) 

10 129 In general, the half life of 



Fig 10 4 Relationship of decay constants of metastable isomers 
to energy differences 


nuclei m the two states, the transitioQ 
from the upper to the lower state will 
be “forbidden “ In other words, the 
probabihty of the transition will be 
small, and, on the average, an appreci- 
able time mil elapse before the excited 
state loses its excess energy and passes 
mto the ground state When this occurs, 
the nuclear state of higher energy js 
metastable and can have a detectable, 
independent existence, nuclear isomer- 


the metastable isomer decreases, as 
expected, as the energy difference be- 
tvreen. it and the ground state increases 
H the logarithm of the half h/e, or of 
the related decay constant A, is plotted 
flgamst the logarithm of the energy 
difference for the known nuclear iso- 
mers, most of the values fall on or 
close to two straight lines (Fig 10 
showing that the half life and the en 
ergy are related The two lines prob* 




281 


Nvrh'ar TTaitsnndaHon and Arliftcial Radioaclivity 


nbly rt-pm^cnf two degrees of forbid- 
dt'im<i:-;s pltU'ed upon the fnuisitions by 
fiifferf.nrcii in the spins of the pairs of 
i'^nmerie nuclei. 

Di:ca.y 3IY Xkut5?on Emission- 

10,130. It inny bo %vondered why, 
in \'i'>v.' of tiic fact that atomic nuclei 
contain protons and neiitron.s. rndio- 
,'ictive decay dws not occur M'ith cmis- 
.‘•ion of tlu>o particle.s, I'he answer is 
that, if a nnclon.s has stifhcicnt cnergj- 
to release a proton or a neutron, that 
i.s, at least 8 Mev. the emi.'^ion usually 
takes place extremely rajiidly, prob- 
ably in much lc.s? than 10"*- second. 


<•', *• SClt) 



22.5 .sec., 4.51 sec., 1.52 .sec., 0.43 sec. 
and, possibly, 0.05 sec., have been iden- 
tified. By making rapid chemical sep- 
arations, it has been found that the 
55.6-scc. period follows the chemistrj- 
of bromine, and the 22.5-sec. period 
follow.s that of iodine. 

10.131. The explanation suggested, 

I in the former case, for extimple, is 
j that one of the products of fission is 
a bromine isotope of high mass num- 
ber, prob.ably Br^'. This decays with 
a lialf life of 55.6 sec. emitting a nega- 
tive beta-particle to jdeld Kr^. The 
latter can be formed in a highly excited 
state with sufficient energy- to permit, 
it immediately to eject a neutron (Fig. 
10.5), and form a stable Kr^® nucleus. 
The observed rate of emission of neu- 
trons is determined by the slow stage 
in the over-all process, namely, the 
decay of the Br^. The half life for 
neutron liberation thus appears to be 
55.C sec., although the actual process 
in which the neutrons arc emitted prob- 
ably occiu-s ven,' rajndly. The 22.5-sec. 
group of neutrons appears to originate 
in an analogous manner from pro- 
( duced in fission; this emits a negative 


Fin. in.."}. Mcchnni^m of rlcc-ny by ncu- 
l.'-on 

In other wonls. the iiarticular nuclide 
wtnild lx* ho un.st.able that it would not 
he regnniti'l a.s having any real exist- 
eni'C. A few insianccs have' been found 
of unstable nuclei which apparently 
flfvay by omitting neutron*-' at a meas- 
urable r.uo. but ihi*^ result is due to 
incidental circumstances. The phenom- 
enon S', of tl'.e greatest .significance for 
tho dc-i’cn of nvjck-a.r energy reactors, 
a'-’ will he in Lat«*r chapters, but 
It h fufih'if'nt to state here that the 
ti-.'-ien o', ur.vnhun. and plutonium by 
!H' acemnp.tniM by the do- 
Ity.-ss cxpnl-jon of n>'n*r<)n.'5. Five or 
--IX hah-hfr |x*rifi»l>i, nr.mely .aS.G see., 


beta-particle, avitb a half life of 22.5 
.•;ec., leaving a highly e.xcited Xe’^ 
nucleus. It is the latter, which in- 
stantaneoush' expels the neutron to 
form stable although the appar- 
ent decay half life is 22,5 sec. 

10.132. A somewhat similar type of 
behavior was discovered in an entirely 
different, connection by L. W. Alvarez 
and bis collaborators in 1948. Upon 
bo.mbarding v-arious light elements 
from o.xygen to cWorinc by means of 
200-Mev deutcrons obtained from the 
lS4-ineh , Berkeley synclirocyclotron, 
the emission of neutrons, associated 
^\-itl^ a half life of 4.1 sec., w'as de- 
tected. After making a scries of care- 
fully jdanned experiments the conclu- 
.rion was reached that the results could 



282 


Sourcebook on Aiomic Energy 


be accounted for by the following 
scheme: 

N17 S— 0" -> 0" + 

« 1 seo 

The unstable species N” is formed in 
the bombardment, this decays with a 
half life of 4 1 sec emitting an elec- 
tron, and leaving a highly excited 0” 


Chap X 

Each nuclide is seen to occupy a square 
those with a shaded background refer 
to stable species occurring in nature, 
while artificial radioactive isotopesha\ e 
a white background. The symbol and 
mass number are indicated m each case, 
as well as the types of decay and half 
liv^ of the unstable nuclides All spe- 
cies on the same horizontal line have 
the same atomic number and hence are 


j 

1 

1 

1 




! 

so 

2" S3 

r.Jf 

sa m 

H 


■ 

■ 



nj 

n 


■ 



1 

2« 

■ 

H 


n 

n 

■■ 

1 


f . 

1 ..n 

1 SI ' 

1 s& 

1 ST 



«W8e*r Of utuTooni 

Fic 10 6. Portion of an isotope chart. 


nucleus. The latter then instantane- 
ously ejects a neutron, with the stable 
oxygen-16 isotope as the final product 

Isotope Chakts 

10.133. The information concerning 
the known isotopic species, both stable 
and unstable, is usually summarized 
in the form of an isotope chart, as it 
is generally called. In one type of chart 
the atomic number Z, that is, the 
number of protons in the nucleus, is 
plotted as the ordinate, against the 
number of neutrons, equal to A ~ Z, 
IV here A is the mass number, as the 
abscissa. A simplified portion of sudi 
a chart is represented in Fig. 10 6. 


isotopic with one another. Nuclides 
with the same mass number, i e , iso- 
bars, are seen to lie on a senes of 45“ 
diagonal lines running from upper left 
to lower right of the diagram 

10.134. Certain features of this iso- 
tope chart Avill be described subse- 
quently; for the present it will be uti- 
lized to consider nuclear transmutation 
and radioactive decay processes 'When 
a particular target nucleus combines 
with a proton, the resulting compound 
nucleus is represented by the nevt 
higher square in the same vertical line 
Similarly, combination w’ith a neutron 
pves a nucleus occupying the 
square to the right on the same hon- 







283 


N'vdcar Trarumufafton and Artificial Radioaclivity 


r,ontnI line. Uptake of a deuleron, 
whiftti con.sistH of a proton and a neu- 
tron, results in a sltift of one position 
vcr( ically upward, and one to tlic right, 
and so on for other particles. Emis- 
sion of a proton, neutron or deutcron, 
of course, re-«uU.s in a reversed of these 
moves on the chart. The expulsion of 
an electron in radioactive decay, i.e., 
negative beta-decay, givc,s a product 
nucleus in which the number of protons 
is increased and the number of neu- 
trons is decre.ascd by unity. The prod- 
uct therefore occupies the adjacent 
upper-left diagonal position from that 
of the p.aront. On the other hand, in 
positive beta-decay, i.e., when -there is 
positron cmi.ssion, or in orbital-electron 
capture, the product nucleus is found 
in the adjoining lower-right diagonal 
square. 

10.135, It is of interest to return, 
at thi.s point, to the case discussed in 
detail in § 10.17 d scg., namely, the 
cotnhinalion of a dculeron with Cu®‘; 
from the chart, the compound nucleus 
i.*'' seen to bo the radioisotope [Zn“], 
undoubtedly in a highly excited state 
with considerable excess energ}-. If 
thi.s cnerg)’ j.s emitted as a gamma ray 
freaction (I)], the product i.s Zn“ in 
its grcnind slate; the chart shows this 
to l>e radioactive, decaying by positron 
einissit>n, or by Jv-captxire, to yield 
stable Cu'~ as the product. A .second 
possibility [reaction (2)] is the ejec- 
tion of a neutron by the [Zn“], le.av- 
ing Zn*‘, -which Is stable. In rc.action 
(3), a proton is emitted, .and hence 
the product i.s On' *; as stated in § I0.9G, 
this c.xhibits branched diKintegr.ation, 
decaying by the cmis-sion of a pasitive 
or a negative lK>ta-part icle, the prod- 
xu't Ix-ing the .-l.-.ble nuclide or 
Zrd\ n-.-'iXTtivftly. Aceortiing to rcixc- 
tir.n (-st, tv,o nciitrous .are c.vpcllcd. 


EO that Zn®^, which the chart, shows 
to be a positron emitter, remains; its 
deca 3 ' product is seen to be stable Cu®l 
If the compound nucleus ejects an 
alpha particle [reaction (5)], the com- 
pound nucleus [Zn“] loses twm protons 
and two neutrons, with formation of 
the stable ]Sii®b The tritinm wncleus 
consists of one proton and two neu- 
trons, and so the product of reaction 
(6) is Cu®^; from the chart it follows 
that tliis decaj's by the emission of a 
positron and is thereb}' converted into 
the stable Ni®* isotope. The last proc- 
ess does not need to be considered since 
it is the reverse of that by which the 
compound nucleus was supposed to be 
formed, in the first place. 

10.136. In addition to the isotope 
cliart described here, in wliich the num- 
ber of protons is plotted against the 
mimber of neutrons for all the knowm 
nuchdes, other types have been used 
for different purposes. For example, 
in one the atomic number Z is plotted 
against the mass number A, or xdee 
versa; and in another, the excess of 
neutrons over protons, that is A — 2Z, 
is plotted against the atomic number 
Z. One of the most recent schemes 
makes use of axes inclined at an angle 
of 60°, the neutron number A — Z be- 
ing plotted along one of those axes 
and the atomic number Z along the 
other; the re.sult is that nuclides with 
the s.amc mass number are found in 
the same vertical row, while each hori- 
zontal row contains species with the 
s.'imc neutron excess A — 2Z.* Each 
t\ 7 >e of chart has features of special 
interest, but, in general, familiarity 
xvith the use of one provides sufficient 
experience for the use of any other. 
It is consequently unnecessary to enter 
into fijrther details here. 




' ^ by Witliara H Sulllvnn (J. Vriley and Soac, Inc., Now 



The Neutron 


Chapter XI 


PROPERTIES OF THE NEUTRON 
Mass op tub Neutrox & iruiss close to that of a proton Smce 

11 1 When, in 1920, E Rutherford evidence was not recorded earlier, 
considered the possible existence of a itwiUbeoutUnedhere The absence of 
particle of unit mass and zero charge charge associated wth the neutron was 
(§ 2 109), now called a neutron, he established, of course, by the inability 
thought that smce it would not be deflect it in electnc and magnetic 
repelled as it approached an atomic fields, the mass was estimated m sev 
nucleus, “it should enter readily into eral ways Suppose a particle of mp 
the structure of atoms, and may unite nioving ivith a velocity t>, colLdes 
with the nucleus ” As indicated in the with another particle, mass ntii which 
precedmg chapter, this expectation has virtually stationary "Hie speed with 
been abundantly confirmed, the nuclei which the latter recoils depends on the 
of virtually all the elements have been direction of recoil relative to that of 
found to interact with neutrons In incident particle, but it is known 
addition, the neutron has served a pur- from mechanics that it will be a maxi 
pose which was entirely unforeseen mum m a head*on collision, that la, 
it provided the key that made possible when the struck particle recoils in 
the achievement of a Iong*sought ob- exactly the same direction as that m 
jective, the release of energy from the which the incident particle approached 
atomic nucleus In this respect, the such a collision, the recoil 

various interactions of neutrons with velocity ti*, which is the maxunum 
atomic nuclei are of the greatest sig- possible for the specified conditions, is 
mficance For these and other reasons given by* 
the study of the production and prop- ^ _ 2mi ^ 

erties of neutrons has attracted much * mi + 

mterest, and the subject merits de- 
tailed consideration If the incident particle were a neutron 

11 2. It was mentioned m § 2 112, and the struck particle were a nucleus 
when reporting bnefly on the discovery of known mass mt, the mass mi of the 
of the neutron by J Chadwick in 1932, neutron could be calculated from cqua- 
that he explained certain apparently tion (11 1) if the velocity v of the 
paradoxical observations of previous neutron before collision, and the maxi- 
workers by attributing them to the mum speed I 2 of the recoibng nucleus 
presence of an uncharged particle with were known 

* TTus IS readily derived from the equations for the conservation of (kinetic) 

13 here and for the conservation of momentum, namely, 

mifi + m5i2 for a head-on collision, Vi is the velocity of the incident particle after the corns 
284 



285 


The Neutron 


11.3. Unfortunately, Chadwick did 
not have reliable data concerning the 
Bpeed of the neutron, and so this had 
to be eliminated from equation (11.1). 
If netj Irons of the same velocity v 
collide with a particle of mass im, the 
maximal recoil velocity t'j of the latter 
is determined by an expression exactly 
analogous to equation (11.1), namely, 


lar to that of the proton, but a more 
accurate determination was desirable. 
Such a determination "was made by 
Chadwick utilizing the energy and 
mass changes involved in the reaction 
between an alpha particle and a boron 
nucleus, in wliich a neutron was ajv 
parcntly liberated. If the reaction is 
of this type, then it should be 




2mi 


?7ij -4* 


( 11 . 2 ) 


sB» + iHe^ + onS 


where nij and v are the same as before. 
Upon dis’idingcquation (11.1) by (11.2) 
it i.s scon that 

Hi ^ (11.3) 

I'i nil + njj 

lluis permitting nq, the mass of the 
neutron, to be evaluated if Wj, ni 3 , t'j 
and t'j arc avtiilnblo. The recoils of 
hydrogen and nitrogen nuclei, after 
l>cing struck by neutrons, were ob- 
FOiwcd in cloud-chamber experiments 
and, from the lengths of the accom- 
j>anying tracks, the maximum veloci- 
ties were estimated to he 3.3 X 10’ and 
'17 X 10' cm. per see., respective!}'. 
’l’he.«c results were known to be ap- 
proximate but they should be .sufficient 
to give sotne indication of the maas of 
the neutron. Thu.s, taking m- and tttj 
to bc- the iiuvs-ses of the hydrogen and 
nitrogen nuclei, namely 1 and 14, 
ri'spectively, on the atomic weight 
scale, the corresponding v.alue-s of Vj 
and naro then 3.3 X 10’ and 4.7 X 10’*; 
upon suhstsUiting these data in equa- 
tion (11.3), the mrjfs r«i of the neutron 
is found to Ik: roughly 1.16, compared 
with unity for the proton. 

11.4. ''liie approximate result ol>- 
taln«xl in this manner showed, at least, 
that the m.'iss of the neutron wjis simi- 

M k'wrf ttsAa ths nuiss (l.TO???) n< 
vstu'.t. 


and since the isotopic weights of the 
stable nuclides B", He^ and N“ are 
available, it should be possible to ob- 
tain the weight of the neutron, pro- 
xdded the nuclear reaction energy (Q) 
were knoum (§ 9.24). The alpha par- 
ticles, obtained from polonium have 
5.25 Mev energy, equivalent to 0.00565 
atomic weight (or mass) units, and the 
energ}' of the product N’* nucleus, 
calculated from its range in a cloud 
chamber, and of the neutron estimated 
from the maximum recoil of a proton 
after collision, were found to be 0.00061 
and 0.0035 atomic weight unit, respec- 
tively. The energy of tlie boron target 
nucleus is negligible, and hence the 
energy change Q of the reaction in mass 
units is 0.00061 + 0.0035 - 0.00565 
= —0.00154. Taking the isotopic 
weights of B” as 11.01244, of He^ 
as 4.00390 and of N» as 14.00751, it 
is scon that the mass of the neutron 
must bc given by 

Mass of neutron 

= 11.01244 -h 4.00390 - 14.00751 

-0.00154 = 1.0073.* 

Using the isotopic weight data availa- 
ble in 1932, Cliadvdck obtained 1.0067 
for the mass of the neutron, but be- 
cause of the uncertainty in the energy 

f accepted, probably because of errors in tbe 



286 Sourcebook on 

terms, he estimated the value to he 
between 1 005 and 1 008 

11 6. Another procedure, which was 
first used by J Chadwck and M 
Goldhaber m 1934, has provided a still 
more precise result for the neutron 
mass The method is based on the 
discovery that gamma rays of suffi- 
cient energy are able to disintegrate a 
deuteron into a proton and a neutron 
(§ 10 46) , thus, 

-b 7 iH* -1- on* 

The minimum energy necessary to 
up iha .is jwjy Jojowd , 

to be 2 21 Mev, which corresponds to I 
000238 mass unit It follows, there- 
fore, that the mass of the deuteron 
plus 0 00238 should give the sum of the 
masses of the proton and the neutron 
The isotopic weights of deuterium and 
hydrogen are 2 01472 and 1 00813, re- 
spectively, so that 

I 

Mass of neutron 

= 2 01472 + 0 00238 - 1 00813 
= 1 00897 

11 6 Since neutrons are involved m 
many nuclear reactions, either as pro- | 
jectiles or as ejected particles, there 
are evidently numerous possibilities for | 
calculating the mass of the neutron, 
provided the isotopic ueig^its of the 
target and product nuclides, and the 
reaction energy are knoivn From an 
examination of the best data available 
m 1950 it appears that the neutron 
mass 18 very close to 1 00897 on the 
physical atomic weight scale It may 
be noted, in passing, that the existence 
of an electrically neutral particle of 
appreciable mass seems to dispose of 
the theory, formerly held by many 
scientists, that all mass is electromag- 
netic m nature (§ 4 20) 


Atomic Energy Chap XI 

lUDioACTiviTy or the Neutrox 

H.7. In the discussion of negative 
beta-decay m § 7 60, it was postulated 
that this type of radioactivity involves 
the conversion of a neutron mto a 
Proton and an electron, together with 
a neutrino The sum of the masses of 
the proton, electron and neutrino la 
Virtually equal to the mass of a hydro- 
gen atom, I e , 1 00813 atomic weight 
Units, since this atom consists of one 
Proton and one electron while the mass 
of the neutrino is negligible It will be 
observed that the total mass is less 
than the mass of the neutron by 
J fm97 - J ^ 
equivalent to 0 78 Mev of energy, and 
So It is possible to wnte 

on> iH’ + + 0 78 Mev 

11.8. The fact that the conveiBion of 
a free neutron into a proton and sn 
electron, together with a neutnno, a 
associated with the hberation of energy, 
Indicates that this process should take 
place spontaneously In this event, 
the neutron would be the simplest rur 
<lioactive species, decaying with the 
emission of a negative beta-particle, 
1 e , an electron, leaving a proton as 
the product Since both the neutron 
und the proton have one-half unit of 
spin (§4 79), it is probable that the 
decay will correspond to a “permitted ' 
ttansition of Fermi’s theory (§7 65), 
hence, the plot of the logarithm of the 
maximum beta-particle energy against 
the logarithm of the decay constant of 
the r^ioactive neutron would be ex- 
pected to fall on the uppermost of the 
Sargent curves m Fig 7 9 The maxi- 
mum energy of the beta particle to be 
expected from the mass change asso- 
ciated with the decay process is 078 
Mev, as seen above, and from the 
Sargent diagram, or the equivalent 
Fermi equation (7 16), the beta-decay 



The Neutron 


287 


constaTit X oi the ne\itron is found to be 
about 6 X 10“^ in reciprocal seconds, 
lienee, according to equation (5.9), 
the half life of the neutron should be 
rougldy 20 minutes. 

11.9. The difhculty in detecting the 
radioactive dec.ay of the free neutron 
lies in the fact that such neutrons are 
readily captured by nuclei; conse- 
qijcntly, the average life of a frqe 
neutron is short in comparison uith 
its cx|>ccted radioactive half-life pe- 
riod . fsV.vcrthclcss, an attempt to study 
the decay of neutrons was initiated by 
L. W, Alvarez of the Rarliation Labo- 
mtory, Berkeley, California, but the 
work was interrupted by the war. 
More recently, the problem has at- 
tracted the interest of A. H. Snell and 
his collaborators at the Oak Ridge 
National Laboratory', and of J. M. 
Robson and lus a.ssociatcs at the Chalk 
River Laboratory' in Canada, The ex- 
j>orimcntal procedure consists in pass- 
ing a strong beam of neutrons tlirough 
a cylindrical tank which has been 
highly ev.acuatcd. /Vn electrostatic field 
is so arranged that any protons re- 
sulting from the beta dcca}* of the 
ncutron.s are deflected and accelerated 
in a direction perpendicular to the neu- 
tron iK'am. By c.ausing those protons 
to fall on a suitable device they can be 
co\mted and the rate of their produc- 
tion detemrined. jVftcr allowing for 
various steondary effects, the rate of 
proton fonnation wrus found to corre- 
spond to a Imlf life of 10 to 20 minutes 
for the fnse neutron, in general agree- 
juent with the calculaterl v.nluc. Al- 
though the results obtained so far .arc 
to be recivuifvl .\v; preliminary', it c.an 
l^' s~ud that they seem to provide sup- 
port for the view th.at the free neutron 
is mdin.ictive, in the sense that it dis- 
intrgrate.s sy>ontaneo!|s1y' with the emis- 
sion of an electron, leaving a proton as 
rrsidual p-artiele. 


Diffraction of Neotbons 

11.10. One of the most striking ar- 
guments for the w'ave-particle duality 
of matter, which was discussed in 
Chapter III, has been provided by the 
diffraction of neutrons. It has been 
known for some years that electrons, 
in particular, and also protons and 
alp^ particles, exliibit the character- 
istic wave property of interference re- 
.sulting in the production of definite 
diffraction patterns (§ 3.41). While 
this evidence for the wave nature of 
matter is quite striking, some objec- 
tion might perhaps have been raised on 
the grounds that the aforementioned 
particles are all electrically charged, 
and that the same phenomena would 
not be observed with neutral matter. 
All doubts of this kind have been 
dispelled by the clear proof that wave 
properties are also associated with neu- 
trons. Tlie first evidence of neutron 
diffraction was obtained by D. P. 
Mitchell and P, N. Powers in the 
United States in 1936, but since that 
time the technique has been very 
gn»tly improved, thanks largely to 
the neutron beams obtainable from 



I diffraction pattern 

j of Eoamm chloride obtained with neutrons 
t from the Oak Ridge nuclear icactor. 



288 


Sourcehooh on AtonCic Energy Chap XI 


nuclear fission reactors A photograph, 
taken at the Oak Ridge National Labo- 
ratory, showing the neutron diffraction 
pattern of a sodium chlonde crystal, 
IS reproduced in Fig 11 1, this may be 
compared vnth Fig 2 7 for the diffrac- 
tion of X-rays 

11 11 Accordmg to the de Broghe 
equation (3 6), the wave length X cm , 
equivalent to a particle of mass nt 
grams, movmg with a \eloeity v cm 
per sec , is equal to h/mv, where h is 
the Planck quantum theory constant, 
6 62 X 10”®^ erg sec Since the energy 
£ of a neutron is essentially all kinetic 
energy, it is equal to and so mv 

in the de B roglie equation may be re- 
placed by the equivalent wave 

length of the neutron is then given by 



Upon msertiDg the value of m, the 
actual mass of the neutron, which is 
approiomately 1 67 X 10~** gram, and 
introducmg the factor 1 60 X 10"*’ 
for converting electron volts to ergs 
(§ 3 30), it follows that 


phenomena with crystals Thisispre- 
cisely what has been found expen 
mentally, and in § 11 83 it will be 
shown how reflection from a crystal 
surface is used to sort out neutrons of 
specific energies or velocities 

11 13. To the chemist, an applica- 
tion of neutron diffraction of excep- 
tional interest is m connection with 
the study of molecular structure Dif- 
fraction of X-rays by crystals and of 
electrons by gases has been very widely 
used to determine the distances 
tween atoms m a molecule But these 
methods have one great drawback 
because the diffraction of X-rays de- 
pends almost entirely, and tiiat of 
electrons largely, on the number of 
orbital electrons of the atom, it is not 
feasible to identify the positions of 
hydrogen atoms with their single elec- 
trons In the diffraction of neutrons, 
on the other hand, it is the atomic 
nucleus which determines the extent 
of diffraction, and m this respect the 
effect of hydrogen is quite considerable 
Hence, neutron diffraction by crystals 
mokes possible the determination of 
mleratomic distances involving hydro- 
gen atoms It may be mentioned, how- 


_6 62 X 1Q-” 

' V2 X 1 67 X 10^ X 1 60 X 
2 87 X 10-* 


Ve 


(115) 


where E is the neutron energy ex- 
pressed m electron volts 
11.12 It 15 of interest to see what 
order of energy would be requisite for 
a neutron beam if the associated wave 
tram were to be capable of diffraction 
by a ciystal The wave length would 
have to be about 2 X Iff-® cm , and 
hence it follows from the equation 
(11 5) that neutrons with energy 
about 0 02 ev should exhibit diffraction 


ever, that a satisfactory application of 
the method requires strong neutron 
beams such as are available only from 
nuclear reactors (Chapter XIV) For 
tins reason a program for the study 
of the internal structures of solids by 
the diffraction of neutrons of low 
energy has been planned and is being 
earned out at the Oak Ridge Na 
tional Laboratory 



The Nciilron 


289 


PROD-UCTIOK I^KD DETECTION OF NEUTRONS 


Nr:trnioK Sources 

11.14. 'Die first recogniecd forma- 
tion of neutrons %vas the result of 
reactions of the (a,«) type, ^vith be- 
ryllium, boron nnd lithium. Subse- 
tjuently, other light elements, such ns 
nitrogen, fluorine, sodium, magnesium 
find aiuminum were found to emit neu- 
trons when bombarded with alpha par- 
ticles. Although none of these can be 
regarded ns strong sources of neutrons, 
from the present-day standpoint, a 
fair jncld of neutrons can be obtained 
from the (a,fl) reaction with beiyllium. 
A convenient means of producing neu- 
t runs is a mixture of metallic betyllium 
with a small quantity of an alpha- 
particle emitter, siich as a radium or a 
polonium comt)ound. A scaled capsule 
containing radium emanation, that is, 
the gas radon, and beryllium provides 
an inexpensive source of neutrons; the 
use of radium, in place of radon, is 
more costly, but the neutron intensity 
is much stronger and more lasting. 

II.IG. Tim neutrons obtained from 
the reaction 

iBc' + jHe« -f erd 

are not monoenergetic; that is to say, 
they do not all have the 6.ame energj'. 
Tne reaction cnorga* of the Be’(a,n)C'* 
pnxess Is about 5.5 IVIcv, and this, less 
I ho nfoil, nnd po-ssible e.xcilation, en- 
erg>' of the C'* nucleus, repre.'^ents the 
minimum onerg)' of the emitted neu- 
iTtm. However, neutrons could be ol>- 
tained with this cnergj- only if the 
incident .alpha particle had zero cnergj', 
and the prob.ability of sucii particles 
entorinp the Ix-rylHum nucleus is quite 
ncghgible, Ine alph.a particles from 
nvfionctive sources have .appreciable 
sn<i of this will ultimately 


appear as energy' of the emitted neu- 
trons. The jdeld from the bombard- 
ment of beryllium by alpha particles 
from 1 gram of radium is about 10 to 
15 million neutrons per second. 

11.16. A number of reactions of the 
(d,n) type have been employed as neu- 
tron sources, the accelerated deuterons 
being generally produced by means of 
a cyclotron (§9.52). With a cooled 
beiyllium target, it is possible to use 
relatively strong deuteron currents, so 
that neutrons are obtained at the rate 
of manj’’ bilbons per second from the 
reaction Be®(d,n)B>'’. Another reaction 
of the same type, but somewhat less 
efficient, is Li^(ii,n)Be®; since the re- 
action cnergj’^ in this case is about 15 
Mev, it is possible to obtain neutrons 
of fairly high energy by bombarding 
lithium udth deuterons of moderate 
speed. 

11.17. It W'as stated in § 10.33 that 
bombardment of deuterium by deu- 
tcrons gives rise to the reaction 

iH* -f ,H* — + jHe’ on' 3.2 Mev, 

and tliis (fi,n) process has been used as 
a source of neutrons, the target being 
ice obtained by freezing heaay* water, 
i.e., solid deuterium oxide (§ 8.71). 
Tlic reaction energy is positive, by 
about 3.2 Mev, and a good yield of 
neutron.s is possible even vrith deuter- 
ons of relatively low energy, for ex- 
ample, doum to 0.2 Mev. 

11.18. Several fight and moderately 
bca%y elements undergo (p,n) reac- 
tions, but only one of these processes, 
namely, 

jLi* -r — ♦ «Be' — 1.62 ?.Icv, 

has been used to any extent as a source 



290 


Soiircehook on 

of neutrons Although the reaction 
energy is here negative by 1 62 Mev, 
the actual threshold energy for the 
protons IS about 1 88 Mev, the ad- 
ditional 0 26 Mev being mainly recoil 
energy of the Be'^ nucleus 

1119. Photonuclear reactions, 
namely, reactions of the ( 7 ,^) type, 
have proved to be particularly valu- 
able for the production of homogeneous, 

1 e , monoenergetic, neutron beams 
(§ 11 85), these are called photoneutron 
sources Processes of the ( 7 ,n) type 
invariably have negative reaction en- 
ergies, consequently, the gamma rays 
must have a definite minimum, or 
threshold, energy before the process 
can take place The energy of the neu- 
tron IS then roughly equal to the energy 
of the gamma radiation used minus the 
threshold energy of the particular ( 7 ,n) 
reaction If these ttvo quantities are 
not very different, the neutrons ivill 
evidently have relatively low energies 

1120 Two photonuclear reac- 
tions mentioned m § 10 45, namely, 
H*( 7 ,n)H* and Be*( 7 ,n)Be*, for whi^ 
the theoretical minimum energies are 

2 21 and 1 62 Mev, respectively, have 

been largely used to produce neu- 
trons Any radioactive species emit- 
ting gamma rays of sufficient energy 
may be employed, in conjunction with 
^ ivsvyAlva® 

as the target “liie half life of the 
gamma ray source should not be too 
short, so that the rate of neutron 
emission may remain fairly constant 
over an appreciable interval of time 
Four such sources, namely, Na’*, Ga”, 
Sb*** and all artificial radio- 

nuclides, satisfy the foregoing require- 
ments The gamma rays from Na” 
can be used with either deuterium 
or berylhum to produce neutrons of 
different energies m the two cases, 
those from are used with deute- 
rium only, in the form of heavy water, 


Atomic Energy Chap X! 

while the radiations from Sb*** and 
La‘“ are employed to interact witli 
beryllium, although the yields m the 
latter case are small 
11 21 A convenient source of neu 
trons, available from the Isotopes Dj 
vision of the Atomic Energy Commis- 
sion, consists of a rod of antimony, 
containing the 60-day Sb’** radioiso- 
tope, surrounded by a berylhum metal 
cup Wlien newly prepared the system 
emits neutrons, of approximately uni 
form (0 03 Mev) energy, at the rate of 
about eight million per second After 
the activity of the Sb“* has decayed 
it can be regenerated by exposure of 
the antimony rod to neutrons m a 
nuclear reactor (Chapter XIV) 

11 22 An unusual type of process 
which has led to the production of 
neutrons of high energy, around 100 
Mev, was discovered m 3047 m the 
course of experiments with deuterons 
accelerated to 200 Mev energy in the 
Berkeley 384-3nch synchrocyclotron 
The neutrons are formed from the deu 
terons as a result of a phenomenon 
called stripping, which is believed to 
occur somewhat in the following man 
ner As mentioned earlier (§1028), 
a deuteron behaves as a relatively 
loosely-bound system consisting of a 
neutron and a proton which are fre 

fhftVritUJ 

tual forces If a high-energy deuteron 
strikes a target nucleus m such a way 
08 to graze the edge of the latter, the 
proton may be stopped off, uhiJe the 
neutron misses and travels on alone 
The proton may be captured by the 
target nucleus, or it may be deflected 
by the magnetic field of the cyclotron 
but the uncharged neutrons continue 
to move in a straight line, thus per 
imttmg their removal as a narrow 
beam The energies of the neutrons 
obtained m this manner range around 
half the initial deuteron energy, so 



291 


The Netilron 


that, wiili 200 Mcv deutcrons, the 
mean neutron energy'’ is about 100 
Mcv. Almost any element be 

u.'^cd as the target material in stripping, 
btit the yield of .stripi)cd neutrons for 
.'I given dcuteron intensity varies wth 
the nature of the target. 

11.23. In recent years there has be- 
come available a source of neutrons so 
powerful that those described above, 
important tho\igh they may be, are 
almost insign ificjuit in comparison. 
Tins source is a nuclear reactor or 
“pile,” in which umnium is undergo- 
ing fission. As indicated in § 10.57, 
this process is initiated by neutrons, 
and it is also accompanied by the 
emission of neutrons. The subjects of 
fission and of nuclear reactors "will be 
treated in greater detail in Chapters 
Xni and XIV. 

Detkctiok of Neutrons 

11.24. Since neutrons do not inter- 
act appreciably nnlb electrons, they 
produce very* little direct ionization, 
namely, about one ion-pair per meter 
of patli, compared with .something like 
a million for a proton noth approxi- 
mately the same energ}'. Direct de- 
tection of a neutron in any instrument, 
such .as a Gcigcr-AlOlier counter or a 
Wilson cloud chamber, which depends 
for its action upon ionization due to the 
entering particle, is thus out of the 
question. Nevcrtliclc.ss, devices of this 
type can Ikj adapted to study neutrons 
by utilizing certain secondary eft eels. 

11.25. Two general principles have 
imn cmploycci in the detection of 
neutrons: first, use is made of the 
chBrgtjd ]jarticles produced by the in- 
teraction of neutrons with v.arions sub- 
stances introfluced into the counter, 
rsnd. second, advantage is ttiken of the 
re-oi! of nuclei of ligiu element.s after 
b-'dne struck by neutrons. In each 

She swondtin' ]tarticlca prodtjce 


ionization in their paths, so that their 
presence immediately becomes etddent. 
The choice of procedure depends chiefly 
on the cnergj’", or speed, of the neutrons 
to be detected; for slow neutrons, vdth 
energies up to a few Kev, the inter- 
action method is mainly used, but for 
fast neutrons, having energies of the 
order of .a hlev or more, the recoil 
principle is generally employed.^ 

11.26. The most common instru- 
ments for the detection of slow neu- 
trons utilize the reaction of these 
neutrons with the less abundant iso- 
tope of boron, B*°; thus, 

jjjio _j_ piji- — > jLjT -}- 2.5 Alev, 

the 2.5-MeA’^ reaction energy being 
carried off by the resulting lithium 
nucleus and alpha particle which pro- 
duce considerable ionization in their 
tracks. In order to take advantage of 
this process, a counter containing bo- 
ron, or a compound of boron, is em- 
ployed. The chamber may either con- 
tain boron trifluoride as part of the 
filling gas or the Avails may be lined 
Avith a thin coating of elemental boron 
or of a solid compound, such as boron 
carbide. Since it is actuallj’’ the 
isotope, present to the extent of less 
than 19 per cent in natural boron, 
AA-liich is involved, better results are 
obtained if the boron compound is en- 
riched in the B’® isotope. Enriched 
boron trifluoride, in the form of solid 
BFj'CaF", can be obtained from the 
Isotopes Division of the Atomic Energy 
Commission. 

11.27. By using a chamber of suit- 
able size, cverj' neutron entering can 
be made to interact A\*ith a B>® nucleus, 
so that the number of counts recorded 
giA'cs the number of neutrons. The 
counter may be of the ionization cham- 
ber tA-pc (§ G.IO), although it is more 
usual to operate it in the proper- 



292 


SouTcehook on Atomic Energy Chap. XI 


tional region (§ 6.21). A Geiger-MiiUer 
counter could be employed, but this is 
unnecessary because of the high energy 
of the alpha particles produced in the 
(n,a) process, and, besides, it is un- 
desirable for it would also count the 
extraneous background of electrons, 
gamma radiation, and so on. 

11.26. It was mentioned in § 6.62 
that the track of an ionizing particle 
in a photographic emulsion becomes 
visible upon development as a line of 
fine grains of silver. Neutrons do not 
affect the silver halide in the emulaon 
directly, but if boron is present in the 
form of a compound, such as borax, 
the charged particles produced in Ae 
reaction with neutrons can be readily 
detected. 

11.29. Another type of neutron re- 
action, namely fission, has been used 
in what have been called fission cAcm- 
bers to detect slow neutrons. Such 
neutrons are able to cause uranium-235 
to undergo fission, and the fission frag- 
ments have considerable ionizing effect. 
A simple type of fission chamber for 
observing neutrons thus consists of an 
ionization chamber of which one elec- 
trode is coated with uranium oxide, 
preferably enriched in the uraniura-235 
isotope. An effective neutron counter, 
devised in 1948 by W E. Shoupp and 
K-H. Sun of the Westinghouse Re- 
search Laboratories, makes use of fis- 
sion in combination udth a scintillation 
counter (§ 6,40). A small amount of a 
uranium compound containing an in- 
creased proportion of uranium-235 is 
mixed with a substance capable of pro- 
ducing luminescence when struck by a 
particle of fission product. Upon mc- 
posure to neutrons, scintillations are 
observed, and these may be counted 
by allowing the light to fall on the 
sensitive cathode of a photomultiplier 
tube, as described in § 6.42. 

11.30. When fast neutrons are being 


studied, it is the general practice to 
make use of the ionization in the track 
of a light nucleus recoiling after being 
struck by a high-energy neutron. For 
this purpose a proportional counter 
may be fflied with hydrogen or deute- 
rium, but a better procedure is to use 
argon, or one of the heavier inert gases 
as the filling gas and to place a thia 
sheet of a hydrogenous material, such 
as paraffin, at one end of the chamber. 
Fast neutrons striking the paraffb 
cause the ejection of protons; these pro- 
duce ionization in their paths through 
the counter, and so can be detected. 
The recoil effect in a cloud chamber 
containing hydrogen may also be used 
to indicate the presence of neutrons, as 
8ho%vn in Fig. 11.2. From the maxi- 
mum length of the paths of the recoil- 
ing protons the energy of the neutrons 
can be estimated. The presence of re- 
coil protons due to neutrons can also 
be made evident by their effect on 
photographic film, and from the lengths 
of the recoil tracks the energy of the 



Fio. 11.2. Cloud tracks produced by pro- 
tons recoiling after collision with neutrons. 
(From Phys. Rev., 60, 1138 (1936)). 


293 


The Neutron 


neutrons can be cjilculated. These pro- 
tons may result from collision of the 
fast neutrons with hydrogen atoms in 
the emulsion or in hydrogenous mate- 
rial, such as water, in the vicinity. 
'Iliis phcnomp.non is utilirod, to some 
extent, for determining the extent of 
exposure of the human body toneutrons 
(§ 18.32). 

11.31, Although uranium-235 under- 
goes fission with either fast or slow neu- 
troni!, only fast neutrons can cause this 
tyj>c of process in the more abundant 
uranium-23S. Hence a fission chamber 
for the detection of fast neutrons can 
be designed using a uranium compound 
which has been depicted in the lighter 
isotope; Fucli a device w-ill respond 
to fast, but not to slow, neutrons. An- 
other po.ssibility is to use a fission 
chamber, without special attention to 
the particular uranium isotope prc.s- 
cnl, surrounded by c-admium or boron. 
Tiic.se inatcri.als null absorb the slow 
neutrons, and so any fission obser\'ed 
in the chainlxir is due to fast neutrons. 

11.32. If it is not required to dis- 
tinguish between fast and slow neu- 


trons, then the particles may be slowed 
doivn by passage through a layer of 
parafiin or of water a few centimeters 
in thickness, as explained below. The 
resulting neutrons can then be ob- 
served by any of the forms of slow- 
ncutron counter described above. 

11.33. A principle somewhat differ- 
ent from those already considered has 
been applied to the detection and 
counting of neutrons of particular en- 
ergies, Certain metals, such as indium 
and rhodium, are able to absorb, very 
strongly, neutrons Ijdng wthin narrow 
energy ranges (§ 11.92); then, as a re- 
sult of a reaction of the (n,y) type, a 
radioactive isotope of the original ele- 
ment is formed. The amount of this 
active material, and hence the number 
of neutrons absorbed, can be estimated 
by observing its beta decay in a G-M 
counter. Alternatively, a tliin sheet of 
the metal, indium for example, in con- 
tact with a photographic film, may be 
used to detect neutrons. The radio- 
activity of the product of neutron in- 
teraction with the indium causes a 
fogging of the film. 


SLOWING DOWN OF NEUTRONS 


Ej^nc Scattering 

11,34. The simplest type of nuclear 
reaction in which neutrons arc the pro- 
jectiles is elastic scattering (§ 10.26). 
'llicro is no formation of a compound 
nucleu.s or of an excited .state, but the 
incident neutron is doprivai of some of 
its energy, which appears as kinetic 
energv-, i.e., cnerg>' of motion, of the 
target nucleus. Die neutron then re- 
coils with less cnergj- than it h.ad liefore 
the impact. Die effect Is essentially 
an elaslic or "bilUani-ball’' Ijme of 
eoULion of the neutron with the atomic 
nucleus; the Interaction may thus bo 
tcKitcd by the oixliimry laivs of me- 


chanics, based on the principles of con- 
EOTvation of energy and of momentum. 
In § 11.2, this approach was used in 
considering a head-on collision in which 
there is a ma.\imum transfer of energj' 
from a neutron to a struck nucleus, but 
in the most general case allowance 
must be made for possible collisions 
at all angles of impact. 

11.36. The calculations are per- 
formed by appropriate integration, 
and tlie result shows that in each 
collision a neutron loses, on the aver- 
age, a definite fraction of the energj' 
it had just prior to the collision. This 
fraction, asmight be e.xpectcd, is greater 



294 


Sourcebook on 

the smaller the mass of the nucleus 
with which the neutron colhdes The 
energy of a neutron, apart from the 
energy equivalence of its mass, is en- 
tirely kinetic in nature, and so it is 1 
directly related to its velocity (§ 3 5) 

It IS seen, therefore, that the speed of I 
a neutron is decreased in a collision 
with an atomic nucleus the extent of I 
this decrease bemg greater the lifter 
the struck nucleus A medium of low I 
atomic wei^t will thus be more effec- 
tive than one of high atomic weight m ' 
slowing down neutrons I 

Thermal Neutrons 

11.36. After a number of collisions 
with nuclei, the speed of a neutron is | 
reduced to such an extent that it has 
approximately the same average kinetic i 
energy as the atoms, or molecules, of ! 
the medium in which the neutron is 
undergomg elastic scattering This en- 
ergy, which is only a small fraction of 
an electron volt at ordmary tempera- 
tures (§ 11 38), IS frequently referred 
to as the thennal energy, smce it de- 
pends upon the temperature Neu- 
trons whose energies have been re- 
duced to values in this region are 
designated thermal neutrons The proc- 
ess of reduemg the energy of a neutron 
to the thermal region by elastic scatter- 
mg is sometimes called ihermakzation 
or, more cooimoafy, sfowrag down It \ 
will be seen m Chapter XIII that the 
slowing down of fast neutrons by col- 
lisions with nuclei plays a significant 
role m the nuclear fission reactors m 
which atomic energy is released The 
material used for the purpose is then 
called a moderator, a good moderator 
reduces the speed of neutrons m a 
email number of elastic collisions, but 
does not absorb them to any great 
extent 

11 37. The suggestion that fast 
neutrons are slowed down by pas- 


Atomie Energy Chap XI 

sage through hydrogen-containing sub- 
stances, such as water or paraffin, until 
their energies reached thermal values 
was made by E Amaldi.O D’Agostino, 
E Fermi, B Pontecorvo, F Rasetti 
and E Segre in Italy in 1935, m the 
course of their important work on the 
radiative capture of neutrons (§ 11 46) 
Soon afterward, P B Moon and J R 
Tillman m England obtained expen- 
mental evidence of this phenomenon 
by showing that neutrons after pass- 
ing through parafiin cooled to about 
— 180*C reacted more readily with sil- 
ver, rhodium and iodine than they did 
at ordinary temperatures Slow neu- 
trons are more easily captured by these 
nuclei than are fast neutrons (§ 11 46) 
Subsequently, several physicists made 
direct measurements of neutron veloci 
ties, and confirmed the fact tbat-the 
values were those to be expected for 
particles with thermal energies 

11 38 It should be emphasized that 
the property possessed by neutrons, 
of having their energies r^uced from 
milhons of electron volts to thermal 
values of a fraction of an electron volt, 
and of Btih being capable of producing 
nuclear reactions, is very remarkable 
Protons, alpha particles and other 
charged particles can be slowed down, 
but they can then no longer interact 
with nuclei, because they are unable 
<0 penetrate the efectrustatft? esergj’ 
bamers In any event, as the positive 
particles are slowed dowm they soon 
pick up electrons, becoming neutral 
atoms and losing their ability to cause 
nuclear transformations Slow neu- 
trons, on the other hand, can enter 
nearly all atomic nuclei (§ 11 47), and 
mduce fission of certain of the heavier 
ones (§ 13 70) It is these properties of 
the neutron, striking and unusual for a 
nuclear particle, which have made pos- 
sible the utilization of atomic energy 

11 39 The average thermal (kinetic) 


295 


The Ni 

energv- of any particle is eq\ml to 
'where h is called the BaUzman7i 
canrtanf* equal to 1.3S X 10"'^ erg, 
or S.61 X 10"^ cv, per degree ar\d T is 
tlu! absolute temperature. ITic normal 
\-aluc of T is njipro.ximately 293° on 
the absolute scale, that is, 20°C, and 
.«o the thermal energy of a particle at 
ordinary temperatures is about 0.03S 
cv. In neutron studies the thermal 
cnerp;j' i.s usually taken as hT,'\ instead 
of yj‘T, so that a thermal neutron 
i.s regarded as one rvith an average 
energ>- f)f 0.025 cv at normal temper- 
atures. It is apparent., of course, that 
the energy of a thermal neutron will 


cittron 

but there is a spread, with small pro- 
portions having vciy^low and very high 
energies. For the purpose of sim- 
plicity, the energj^ distribution vdll be 
ignored in the subsequent discussion. 

11.40, Since the mean fractional de- 
crease of cnerg}' per collision can be 
determined, as indicated above, it is 
possible to calculate the number of 
collisions necessarj'’ to reduce the en- 
ergy' of a neutron from a particular 
value, say 1 INIev, to the thermal 
energ}' of 0.025 ev at ordinary temper- 
atures. The results obtained in this 
manner for a number of the ligliter 
elements are quoted in the table. 


.Sl.OWINfl Dowx OK 1-MeV NEWniON'S 


Jvlcinenf 

H 

1 , , 

i D 

1 

lie 

lie 

c 

0 

Mans number 

1 

2 

BH 

■■ 

12 

16 

FmctSynal energy loss (vrr colligion 

0.G3 

0.52 

0.35 

O.IS 

0.14 

0.11 

rollicion'f for thermnlization | 

18 

25 

42 

90 

114 

150 

Capture rro'-s gectinn {barns) ! 

0.3 

0.001 

0 

i 

0.01 

0.005 

1 

0.002 


ticjM'ud on the temj^eraturc of tbc .‘»ur- 
rouudtugs; thermal neutrons iu a mi- 
flcar fi.ssion reactor will liave appr»?ci- 
nbly larger energies tl\nn such neutrons 
in {he nlrnos'phere because the temper- 
ature is higher. In any event, oven at 
a .‘•■pceifir ternpcrattire, not all thenual 
ninUrons will have the same cnerg>' 
(or velucHy); just a.« with moleculo.s of 
.n pas, there is a distribution of energies, 
usually spivkeu of s\.s the .^faxirell disfri- 
hydhn.'l The energies of most thermal 
!5eutr.n>s lie elo^e the mean value, 


11.41. It is seen that a 1-Mev neu- 
tron will, on the average, have to 
make about IS collisions with hydro- 
gen nuclei before its energj’^ is re- 
duced to thermal values, but approxi- 
mnieh' 114 collisions will be neces- 
sarj- with carbon nuclei to bring about 
the same energy decrease.! Tlio num- 
ber of collisions necessarj’ to thermalize 
a 1-Mcv neutron olmously increases 
with the ma.'^s number of the nucleus 
with which it collides; hence moder- 
ators for slowing down neutrons should 


’ fi.r 1 IkiUsnyittri, tlu* Au'-trbn mathematical phyaewt, who made important 

*** the ametJC tiic<'ry of and related subjeots. * 

fJy dieniral neutrons Knve Ihk energy than 

1 <55 2.'25, wl.o, in ISCO. devcloi>ed the theoretical cqua- 

trva hr tb< diCnhutJon ot cnrTK\- {or %fhx>itv) among jma molecules. ^ 

I do no; t.al e into accx>unt the pncsible effect of m-stal gcaUerinc (5 11 101 

for ejampev feat! aho the tnereased .««itterinKof flow neutroas bv bound hvdro-cn’ 
nn p^ramn, factors arv in^portaat, but they do not affect the main 


trj 
































296 


Sourcebook on Atomic Energy CAop XI 


consist of the bghter elements In 
order that the thennahzation proc^ 
may take place as rapidly as possible, 
it IS desirable to use a solid or liquid as 
moderator, the nuclei are then packed 
more closely than in the gaseous state, 
and collisions with neutrons occur more 
frequently Substances hke hquid wa- 
ter and paraflan wax, the latter con- 
sistmg of hydrogen and carbon, are 
thus cheap and convement materials 
for slowing down fast neutrons But 
neither of these is altogether satisfac- 
tory for use as a moderator, because 
there is an appreciable probabihty that 
the slow-moving neutron will react 
with, and hence be absorbed by, a 
hydrogen nucleus In other words, the 
hydrogen nucleus has a moderately 
high cross section (§ 10 70) for the 
absorption of slow neutrons This is 
shown by the approximate capture 
cross sections for thermal neutrons 
given m the last line of the table 
Nevertheless, in one type of nuclear 
reactor, ordinary water acta as the 
moderator for slowing down the neu- 
trons (§ 14 97) 

11 ^ An ideal moderator, m the- 
ory, would be hqmd helium, smce this 
element appears to be the only one that 
does not absorb neutrons under any 
conditions, but since the temperature 
would have to be extremely low, use of 
Jiqmd helium is, obviously, not practi- 
cal Of the remaining elements in- 
cluded in the table, deutenum, m the 
form of deuterium oxide or heavy wa- 


ter, beryUium and carbon offer djs 
tmct possibihties, and heavy water 
and carbon, as graphite, are actually 
used as moderators in nuclear reactors 
Because of its relative rarity, beryUium 
has not been largely employed as a 
moderator, but it may find applica- 
tions m nuclear reactors of the future 
It %vill be noted that the light elements 
lithium and boron have been omitted 
from consideration, the reason is that 
their nuclei have such high absorption 
cross sections for slow neutrons that 
these substances have no practical value 
as moderators 

11 43 The speed of a 1-Mev neu- 
tron 18 about 1 4 X 10* cm per sec., 
and this is decreased to about 2 2 X 10* 
cm per sec , when the energy of the 
neutron is reduced to that of the ther 
mal region However, even a "slow,” 
thennal neutron still travels at a rate 
of appreciably more than a nule pei 
second After a neutron has been 
slowed down, a process which takes a 
very smaU fraction of a second, it still 
contmues to move about the medium 
coliidmg with nuclei, until it is either 
captured or it escapes The motion or 
diffusion of thermal neutrons is of 
great importance m connection with 
the design of nuclear reactors The 
theoretical treatment of neutron diffu- 
sion, which mvolves mathematics of 
an advanced character, is somewhat 
similar to that used by engmeers m 
the study of heat flow 


NEUTRON REACTIONS 


Radiative Capture 
11 44. The neutron, being electri- 
cally neutral, is not subjected to elec- 
trostatic repulsion, as are charged par- 
ticles, when it approaches an atomic 
nucleus In fact, as the neutron ap- 


proaches the nucleus, attractive forces 
begin to operate and the neutron may 
be captured with the formation of a 
compoimd nucleus Because of the 
absence of repulsion, there is no energy 
barrier preventmg the access of the 



297 


The NdUrem 


neiilron to an atomic nucleus, and so 
even the slowest neutrons, such as the 
thermal neutrons described in the pre- 
reding section, can be readily captured. 
For the nuclei of mo.sf elements, other 
(lian the very lightest, tlie addition of 
a neutron results in an increase of 
energ^' equal to about. 8 Mev (§ 12.7), 
plu.s the kinetic enerf^y of the incident, 
neutron. Hcticc, even when a thermal 
neutron, with enorp^- a small fraction 
of an electron volt, is captured the 
compound nucleus formed will u.suall}' 
be iti a hiph-enerpyq excited state, 
which attains relative stability by the 
ejection of a proton or an alpha particle 
or by emitting the cxcc-s-s energy' as 
gamnia radiation. Tlio rcsidiial nu- 
cleus i.s not jilways completely stable, 
for it is frequently radioactive. 

11.45. The first nuclear transmuta- 
tion.s brought about by neutrons were 
reported in 1932 by N. Feather in 
England, and by W. D. Harkins, D. M. 
Gans and H. W. Newson in the United 
Btatc.a. Fast neutroms were employed, 
atid (n.a) reactions wore observed with 
nitrogen, oxygen, fluorine and neon 
nuclei ju; targets. In 1934, D. E. Ijca 
in England oljservcd gamma rays when 
hydrogotwontaining substance.s were 
bombarded with fa,st neutrons; it was 
suceesttxl that those represented the 
encrji^y’ libr-nitod in the formation of a 
dr-uteron from a neutron and a proton, 
s!) th.at the nc.action wa.s a .dmplc t\q>e 
of mdiative capture, i.e., («, 7 ), process. 

11, 40. The gre.at importance of the 
radiative capture reiiclion with neu- 
troms iK-canic apparent from the work 
of E. Fcnni and his collaborators in 
Italy during 1934. .\t that time the 
known ttmis-mutation reactions in- 
voU'ixl only the lightest elements, but 
tie y fcauni that of .some sixty elements 
bomhard-'xl with neutrons, about two- 
tlurvF, ranging fn>m low to high atomic 
rmndHTs, we.n* converted into radio- 


active isotopes of the target material. 
In the course of these studies, the 
Italian scientists referred to in § 11.36 
noted that if the neutrons were passed 
through water or paraffin they became 
much more effective in radiative cap- 
ture (n, 7 ) reactions. This extremely 
significant phenomenon was attributed 
to the slowing down of the neutrons by 
the hydrogen-containing material, the 
.slow neutrons being more readily cap- 
tured by the target nuclei. Subse- 
quently, measurements of absorption 
cross sections with neutrons of various 
speeds completely confirmed this sug- 
gestion (§ 11.91). The discovery of 
transmutation by slow neutrons is 
historically significant for it led ulti- 
mately to the realization of nuclear 
fission, and consequently to the prac- 
tical possibility of utilizing nuclear 
energ,Y. 

11.47. The radiative capture reac- 
tion with slow neutrons is probably 
the most common nuclear proces.s, for 
it takes place with nearly all elements. 
As stated in § 10.42, the transmutation 
product is an isotope of the target ele- 
ment with a mass number one unit 
larger. The energies, i.e., the Q values, 
of these i-eactions are always positive, 
and much of this excess energj'' is 
emitted !is gamma rays which are some- 
times intcmally converted (§7.84). 
Tile simplest {n,y) reaction with slow 
neutrons occurs with hydrogen as the 
target nucleus, thus, 

iH* > iH' d" Y> 

the product being deuterium. This is 
the reaction whereby the absorption of 
slow neutrons by liydrogen, in water 
or paraffin, mentioned in § 11.40, takes 
place. The reaction is seen to be ex- 
actly the reverse of that described in 
§ 11.19 for the production of neutrons 
by the action of gamma rays on deute- 



298 


Sourcebook on Atomic Energy Chap XI 


nxun Since the minimum energy nec- 
essary for the latter reaction is known 
to be 2 21 Mev, it follows that m the 
(n, 7 ) reaction with hydrogen, the en- 
ergy of the gamma radiation will have 
at least this value The emiraion of 
such radiation, of relatively high en- 
ergy and penetrating power, has been 
confirmed experimentally Cognizance 
must be taken of this fact when water 
or other hydrogenous mateiial is used 
in connection with a nuclear reactor, 
either as moderator, as a coohng agent, 
or as a shield to prevent escape of 
neutrons (§ 18 49) 

11 48 Since the capture of a neu- 
tron, followed by the emission of 
gamma radiation, must be associated 
with an increase m the neutron-to- 
proton ratio the product of an (n, 7 ) 
reaction is bkely to be radioactive, 
especially if the ratio of neutrons to 
protons m the target nucleus is already 
near the upper limit of stability for the 
given atomic number Consequently, 
radiative capture reactions have been 
extensively used for the production of 
radioisotopes (§ 16 20 et seq ) A ra- 
dionuclide obtained m this manner 
will emit a negative beta-particle,* for 
this mode of decay means that the 
neutron is replaced by a proton, thus 
bringing the neutron-to-proton ratio 
back into the range of stability Over 
a hundred (n 7 ) reactions leading to 
beta active isotopes have been re- 
ported Two of these, m which Rh*®* 
and In’“, respectively, are the target 
nuclei, 1 e , 

isRh'*” + on* ^sRh*'’* (44 sec ) -h 7 
-f- on* — + 49 ln**® (54 mm ) + 7 , 

are of particular mterest since they are 
used for the detection of neutrons of 


more or less specific energies, as men 
tioned m § 11 32 

11 49 Perhaps the most notable of 
all (n, 7 ) reactions, to which reference 
only unll be made here, as it will be 
treated more fully in later chapters 13 
that undergone by uranium 238, thus 

kU“s + on* -> + 7 

The product uranium-239 is a negative 
beta-emitter with a half life of 23 min , 
decaying by the process 

sjU*” ssNp«® -1- 

the daughter being an element of 
atomic number 93, called neptunium 
(Np), which does not at present exist 
m nature to any detectable extent 
Neptumum-239 is itself beta active 
(half life 2 3 days), as follows, 

„Pu«» -b .A 

the product bemg plutonium-239, a 
relatively long-lived alpha emitter 
(§ 15 24) 

Ejection of CaAROED Particle 

11 60 It has already been stated m 
several occasions that a charged par 
tide, such as a proton or an alpha 
particle, is hmdered from leaving an 
atomic nucleus by the electrostatic re- 
pulsion bamer Hence, processes of 
the (n,p), (n,d) and (n,a) types can 
take place only when the mcident neu 
tron Buppbes sufficient energy to ove^ 
come the force binding the charged 
particle m the compound nucleus and 
also to permit it to escape It is conse- 
quently to be expected that these re- 
actions wU, m general, require fa^ 
neutrons, and this has been found to be 


* Several instances have been reported of p<»itive beta-active or K-capture products fro® 
(n y) processes, in each case the neutron to-proton ratio of the target nucleus is near tn 
lower limit of stability for the particular msra Dumber (| 12 23) 



299 


The Nculron 


tnie, with some fcv.' exceptions which 
vrill i>c considered in due course. Fur- 
tiicr, since the force of electrostatic 
repulsion between a nucleus and a 
cliarged particle incrca.'^o.s noth the 
ntomic number, that is, mlh the posi- 
tive charge, of the former, the requi- 
.'<-ito neutron energy becomes greater 
with increxusing atomic number of the 
target material. 

11.61. Nviclcar procc-sse.s of the (ji,p) 
ty{>e are usuallj" as-sociated with a neg- 
ative reaction cnergv’ of the order of 
1 Mev or more, anil so fast ncutron.s 
having this sunouni of energy', at least, 
are nccessnrj'. I'hr a few light nuclides, 
lle^ .and in particular, the energy 
change for the (n,p) reaction i.s posi- 
tive, inste.nd of ncgiitivc, and in ad- 
dition, the potential barrier inhibiting 
the escape of the proton is relatively 
low Ijccaupc of the small atomic num- 
bers of the nuclei. In these instances, 
thc{fi, 7 )) processes, namely, Hc*(n,p)rP 
and N'*(u.p)C'S rc.spcctivcly, can 
therefore take place with .slow neu- 
trons. nie latter reaction is of special 
interest and importance, for it is used 
in the preparation of the radioxictivc 
C'‘ isotope of carbon. It wll be seen 
in Chapter XVI that this nuclide has 
proveri of exceptional value in the 
.study of proccssc.s occurring in living 
('rganism*.-, and apprcci.able quantitic.s 
are made by exposing solid calcium 
nitnUo to the intense neutron concen- 
tration of a nuclear fission ro.actor. By 
the .netion of these neutrons the 
atom is transmuUjd into one of C“, 
by the (n.p) rcrjction mentioned above. 
?dosl of the carbon is released its car- 
hoii dioxide, wliich Ls nbsorlxxl in bar- 
ium hydroxide solution to form radio- 
active b.irium carbonate. 

* A hyr cxiv'pibrxnl arc 
or tnKiha.'i K-c 

s*- hi llii* Rrtfjori'iii 


11.62. Because the gain of a neutron 
and the loss of a proton means an 
increase in the neutron-to-proton ratio, 
most of the products of {n,p) reactions 
are radioactive, decajdng wdth the emis- 
sion of a negative beta-particle.* It is 
to be noted that the nuclide resulting 
from the decay is identical with the 
original target material, and this fact 
permits some interesting light to be 
shed on the energy changes of the (n,p) 
reactions. 

11.63. Consider, for purposes of il- 
lustration, the N”(n,p)C^^ reaction, 
namely, 

7N« ri- on> -> eC» -f ri- <3, 

the radioactive C'* decaying by the 
process 

cC'* —* + -iri* ri- Fmiut, 

so that the final product N” is identi- 
cal with the initial target nuclide. The 
reaction cnergj' of the (n,p) process is 
represented by Q, while the energy 
change accompanying the beta decay 
is equivalent to (§ 7.48), the max- 
imum energy of the emitted beta par- 
ticles. 

11.64. Tlie over-all result of the t^vo 
processes is obtained by adding the 
two foregoing equations and cancelling 
o\it such species as appear on both 
.sides; the net elTect is seen to be 

-f _,e0 ^ Q ^ 

In other words, as a con.sequencc of 
the (n,p) reaction and the en.suing beta 
, decay, a neutron has been converted 
! into a proton and an electron, together 


;no-.vn m which thr prcxluct of an (n.p) irarijon Is a posUiv 
&p\ure; ti.5 ncutron-ln-proloa mrio? of the target spociis? ar 
* luv.a.vv't in § II .?S, at the iowrr iiniit of stability for the p.v 



300 


Sourcebook on 

•with, of course, a neutrino in, the 
second stage The energy change of 
this process is knoivu to be 0 78 Meir 
(§ 11 7) and so it folloiv’s that Q + 
must have this same value 

11 66 The result, derived above by 
taking a specific example, is completely 
general for all cases of the type under 
consideration The sum of the energy 
of the (n,p) reaction and the maximum 
energy of the beta decay which follows 
must me\ itably add up to +0 78 Mev, 
so that the (n,p) reaction energy Q is 
equal to 0 78 — In the majonty 
of instances is larger than 0 78 
Mev, so that the (n,p) reaction energy 
IS negative, as stated above, but it 
happens that the energies of the beta 
particles emitted by tntium (H*), by 
carbou-14 and by 6ulfur-35 are excep- 
tionally low, 0 015, 0 154 and 0 169 
Mev, respectively Hence the reac- 
tions He*(n,p)H», and 

Cl“(n p)S*®, m which these species ore 
formed, are accompanied by positive 
energy changes, thus making it pos- 
sible for the reaction to occur with 
neutrons of low energy 
11 66 As indicated m § 10 43, proc- 
esses of the (n,d) t3T3e should require 
neutrons of lugh energy, but such re- 
actions are somewhat unexpected, in 
any event, smce the emission of a 
neutron and a proton might be more 
pruiuiiV i^hvenJAefess, (n,a'f reactions i 
have been detected as a result of 'the I 
bombardment of elements of low, me- I 
dium and high atomic number by 90- ■ 
Mev neutrons It appears that the 
incident neutron moves through the 
target nucleus so rapidly that it some- 
times carries a proton before it, eraei^- 
ing as a deuteron There is some possi- 
bility that an (n,0 reaction takes place 
m an analogous manner It should be 
pointed out, in accordance with the 
statement in § 10 56, that these re- 
actions 'With high-energy particles do 


Atomic Energy Chap XI 

not involve the formation of a com 
pound nucleus m which there is a 
redistribution of energy 
11 67. If it were not for the elec- 
trostatic potential energy hamerwLicli 
makes it difficult for an alpha particle 
to leave the compound nucleus, an 
(n,a) reaction with a given target ma- 
ten^ would usually be more probable 
than the corresponding (n,p) process 
The reason is that the removal of an 
alpha particle from a nucleus generally 
requires about 4 Mev (§ 10 9), whereas 
8 Mev are necessary to detach a pro- 
ton Smce the entering neutron con 
tributes about 8 Mev, the reaction 
energies for (n,a) processes usually 
have positive values When the target 
element has a low atomic number, the 
potential energy barner tending to hold 
back the alpha particle is not too bi^, 
and hence (n,a) reactions might be ex 
pected to take place when such ele- 
ment are bombarded with slow neu- 
trons Such IS actually the case with 
boron-10 the reaction B'®(n,a)Li’' being 
employed, as staled in § 11 25, for the 
detection of slow neutrons 
11 68 Another process of the same 
type has been observed when low 
energy neutrons react 'wuth the lighter, 
less common Li® isotope of lithium 
the (n,a) reaction, ■with an energy 
change of about 4 5 Mev, is 

,Li* -f iH* + sHe*, 

so that the product is tritium, the 
hydrogen isotope of mass number 3 
ITie bombardment, by means of neu 
trons from a nuclear reactor, of lithium 
ennched m the hghter isotope, offers 
the possibility of a method for pro- 
ducing this interesting isotope of hy- 
drogen m quantity 

11 69 As the atomic number of the 
target nucleus mcreases, the height of 
the potential barner rises rapidly, and 



The Neutron 


301 


emteion of an alplm particle becomes 
less probable. In order for the (n,a) 
process to take place, additional cn- 
erpy must be supplied in the form of 
kinetic energy of the neutron projectile; 
lienee, for elements of higher atomic 
number the (n,a) reaction is possible 
only if high-energj*, that is, fast, neu- 
trons arc available. Processes of the 
{n,a) typo arc not common -with target 
materials of atomic number exceeding 
•10, although mercury', thallium and 
lead, atomic numbers 80, 81 and 82, 
respectively, have been reported to re- 
act in this manner. As a general rule, 
when the neutron has sufficient energy 
to make the (n,a) reaction possible 
noth an element of high atomic num- 
ber, other i>rocesscs, such as (ft,2n), 
take place in preference. 

11.60. In an («,«) reaction, one ncu- 
t ron enters the system but two neutrons 
and two protons leave, in the form of 
an alpha particle; consequently, the 
profluct nucleus has one neutron and 
two protons lc.ss than did the target. 
'Hint i.s to fay, the noutron-to-proton 
ratio of the product i.s greater tlmn that 
of the bombarded species. It is not 
surprising therefore that most of the 
nuclides formed in {n,a) procc-sses are 
nulioa'ctivc, dccajing vdth the emis- 
sion of a ncR.ativc beta-particle. Tu*o 
examples, mentioned in § 10.43, arc 

d- t’d tX’* + sHeS 

followed by the decay, uitli a 7.3-sec. 
Imlf life, 

-v -f 

and 

r Zn*"* -b fU* nisi” -i- tile*, 

folloui'ti by rise decay, witli a 2.6-hour 
half life, 

rAT" -V 


Emission of Neutrons 

11.61. For elements of low atomic 
number the first e.XGited energy level 
of the target nucleus is usually about 
1 Mev or more liigber than the ground 
state. Consequently elastic scattering 
of neutrons, without the formation of 
an axcited state of the target element 
(§ 10.26), is more probable than in- 
elastic scattering with the lighter ele- 
ments, unless the neutron energy' ex- 
ceeds 1 Mev. With increasing atomic 
number the minimum excitation en- 
ergy' of the nucleus decreases to about 
0.1 Mev (§ 11.103), and so neutrons 
with energy' in excess of this amount 
e.xhibit inelastic, as well as elastic, 
scattering with the heavier elements. 
In (n,n), i.e., inelastic scattering, re- 
actions the fast neutron first unites 
with the target to form a compound 
nucleus; a neutron of lower energy' is 
then emitted, leaving an excited state 
of the target nucleus as residue. 

11.62. Two types of inelastic (n,n) 
scattering may' bo distinguished . In the 
first, most common, category', may be 
placed processes which should strictly' 
be referred to as (11,717). The transition 
of the excited state of the nucleus to 
the ground state, accompanied by the 
emission of the excess energy' as gamma 
radiation, takes place within such a 
short time inten'al after the ejection 
of the neutron that the excited state 
has virtually no independent existence. 
The expulsion, from the compound 
nucleus, of the neutron and the gamma 
ray photon may’ thus be regarded as 
taking place almost simultaneously'. 
Of greater interest, however, is the 
second type of inelastic scattering, 
which might, with more justification, 
be calierl (n.ij) procc-sses. In these 

I cases the tran.rition from the excited 
I state to the ground state of the target 
j nucleus is **forbiddcn.** The c-xcit<Ki 
I state is then a metastable state, i.e.. 



302 


Sourcebook on Aiomic Energy Chap XI 


an isomer, of a stable nuclide, it has a 
fairly long half life, and decays by the 
emission of gamma rays at a measurable 
rate (§ 10 123) Four nuclides exhibit- 
ing this (n,n) type of behavior are 
Agi" and In”* 

11 63 If an mcident neutron has 
about 10 Mev energy, it contnbutes a 
total of approximately 18 Mev to the 
system, since the bindmg energy of a 
neutron is usually in the vicinity of 
8 Mev, except for the lightest elements 
Sufficient energy is consequently avail- 
able to make it possible for two neu- 
trons to be ejected from the compound 
nucleus Hence with neutrons of 10 
Mev energy or more, processes of the 
(n,2n) type are observed, the efficiency, 
or cross section, increasing rapidly with 
mcreasing energy of the incident neu- 
tron Such reactions have been de- 
tected with a large number of nuclides, 
ranging from carbon to uranium, two 
examples are 

eC” + on* — * #C** + on* + on' 
and 

jjXJJss ^ 4* cn* -f- on*, 

the residual nucleus being isotopic n ith, 
but one mass unit lighter than, the 
target in each case 
11 64 About tw o-thirds of the one 
h'CiTjdcied -oi nzi Tadwisc/lopeB -pTwinced 
m (n,2n) processes decay with the 
emission of a positi\ e beta-particle, or 
by the equivalent orbital-electron cap- 
ture (§ 10 106) This IS in harmony 
wath what might be expected, since the 
reaction is accompamed by a decrease in 
the neutron to-proton ratio, the change 
IS rectified by the conversion of a pro- 
ton mto a neutron, resulting from the 
ejection of a positron or the capture of 
an orbital eleetrcm Thus, the decay of 
the 20 5-mm C** occurs by positron 
emission 


bC” -♦ +ie° -f sB**, 

whereas Hg*®^, obtained in the 
Hg***(n,2n)Hg*®^ process decays by K 
capture, 

soHg*®’' + _ie“ — » g7Au‘”, 

both final products being stable nu 
elides W ith elements of relatively high 
mass number, the neutron-to proton 
ratio IS normally considerably in excess 
of unity (1 12 20), and the net loss of 
a neutron in the (n,2n) reaction does 
not necessarily lead to positive beta- 
decay In fact the emission of a nega- 
tive beta-particle occurs m a number 
of instances, especially where the neu 
tron-to-proton ratio of the onginal tar 
get nuclide, Ge", Cd**<, Ce*« and 
for example, is at the higher limit of 
the stability range 

11 66 If the energy of the incident 
neutron approaches 30 Mev, it is evi 
dent that the compound nucleus should 
be able to eject three neutrons or even 
two neutrons and a proton There 'mil 
probably be sufficient energy available 
to overcome the electrostatic potential 
barrier which tends to prevent the 
escape of the proton, m the latter case 
A few examples of (n,3n) and (n,2np) 
reactions have been reported, and many 
more probably remam to be discov 

eied VfbenmtfcdTotGttf’Jtsy 

ergies, m the region of 100 Mev, are 
used as projectiles, nuclei of moderate 
mass number may undergo spallation 
(§ 10 59), while those of high mass 
number, notably bismuth and lead, 
suffer fission The subject of transmu 
tation by very high-energy neutrons is 
stiU m its infancy, for it is only quite 
recently that such neutrons ha\e be 
come available for expienmental pur 
poses 

1166 Nuclear fission can be induced 

m certain nuclides, such as uranium- 


The Neutron 


235, by neutrons of almost, any energ;,-, 
but in otficr cases, fast neutrons are 
necessarj'. These processes, which arc 
s-oinetimcs represented by the symbol 
(nf), will 1 k! discussed in some detail 
in Chapter XIII. 

NncLKAit Cno.s.s Sectioks fok 
NE urnoK Reactioks 

11.67. The probability, or efficiency, 
of interaction between a given nucleus 
and an incident neutron is conveniently 
represented, as stated in § 10.70, hy 
the miclear cross section. This quan- 
tity may be regarded as the effective 
size of the t.argct jiresentcd by the 
particular nuclcuR to the bombarding 
neutron. A great deal of work has 
already been done in connection with 
(he detennination of nuclc.ar cross scc- 
tion.s for neutron reactions, but much 
still remains to be done, for the subject 
has coirsidcrablc practical and tlrco- 
relical significance. Tlie importance of 
(he oros.s section in relation to the de- 
velopment of atomic nuclear cnergj' 
may well be .summarized in the words 
of A. II. Snell of the Oak Ridge National 
laboratoiy. In an cs-say on Contem- 
porary Neutron Physics, published in 
the joumnl Scinwc in 191S, he said: 

. a new scale of values of sinic- 
tural inateri.als has .spning tip; if a 
.‘'Uggestion i-s made as to a new sul>- 
stance for use as part of a reactor, the 
fimt question askc<l is not ‘What is the 
tensile .strength?’ or ‘Wlint is the cost?’, 
but rather ' Wliat is the cross section?’ ” 
Hut even l>cforo 1939, when the re- 
lease of .ntoraic cnergj' was an uncertain 
tiossibiiity that might he realized in 
the indefinite future, the study of nu- 
rSoar crass s.ections for neutron reac- 
tions, jxfcne<I to brioffy as nni/rwi 
cre-ff nttnreted considerable 

nttentueu fflie reawn v,-as that it was 
th.oughl. with some justiffcation, that 
the infonnation would contribute to a. 


303 

better understanding of the compIe,xi- 
ties of nuclear structure. 

11.68. IMicn physicists, around 1934, 
first reported measurements of neu- 
t ron cross sections, the results appeared 
to be erratic and conflicting. M fur- 
ther experiments were made it soon 
became clear that the cross sections 
for fast and slow neutrons w'ere often 
verj' different. However, even this dis- 
tinction was not entirely sufficient to 
bring order out of the chaos. It is now 
realized that a proper understanding of 
the subject requires a complete study 
of the cro-ss sections of a given nuclear 
species for interaction with neutrons of 
various energies, from the lowest val- 
ues, wliich might go doum to 0.001 ev, 
to values as high as 100 Mev or more. 
Much work has been performed with 
"slow neutrons” or “thermal neu- 
trons,” but the results, although they 
may have some practical use, are not 
of fundamental significance. It wnll be 
seen shortly that a small difference in 
the neutron energy may sometimes be 
accompanied by a very large change 
in tlic cro.s.s section; consequeiitlj”, it is 
often necessary to specify the precise 
energy for which tlie cross section is 
measured. A general description of the 
neutron energy, such as is implied by the 
tcmi "thermal neutrons,” is then in- 
adequate. Further, most of the meas- 
urements made hitherto have been 
with the elements, usually consisting 
of a mixiure of isotope.s, as they occur 
in nature. There are good indications 
Uiat for certain neutron energies the 
cross .'cction.s of isotopes often differ 
considerably, and hence it udll ulti- 
mately be neccs-sarj' to obtain data for 
each individual nuclide. 

11.69. .-Vnother factor which mu.st 
lx? taken into consideration is that a 
given nucleus generally has a different 
cross .action for each type of neutron 
reaction in which it can take part. For 



304 


Sourcebook on Atomic Energy Chap Xl 


example, there is a cross section for 
elastic scattering, another for inelastic 
scattenng and still others for radiative 
capture (n,y), ior proton enussion (n,p), 
for alpha particle emission (n,a) and 
so on With elements of hi^ atomic 
number, such as thorium, uranium 
and plutomum, there are also fission 
cross sections In due course, the sepa- 
rate cross sections for the different 
processes to be taken into consideration 
will be determined, but m the mean- 
time a rough subdivision into scattering 
and absorption cross sections may be 
made The former is the sum of the 
cross sections for elastic and inelastic 
scattering, and the fatter is the totaf 

A 


toutec jj- oereemt 

Fio 11 3 Determination of absorption 
cross sections 

cross section for all processes m which 
a neutron is captured and another par- 
tide (or particles) emitted The sum 
of the scattering and absorption cross 
sections is the total neutron cross sec- 
tion for the given nuchde 
11 70 The most direct procedure for 
determining total cross sections is to 
make use of the transmission method 
upon which equation (10 1) is based 
Tllie experimental arrangement is de- 
picted m outlme m Fig 11 3, it con- 
sists of a neutron source and a detector, 
between which can be placed a slab A 
of the experimental matenal If Jo is 
the neutron intensity reaching the de- 
tector in the absence of the absorbing 
matenal, and I is the value when the 
slab of thickness x, contammg JV atoms 
per cc , IS present, thenlt follows, upon 
taking the loganthm of equation (10 2) 
and rearrangmg the result, that 


<r 


2 303, 7c 


I’ 


(116) 


where the factor 2 303 is used to coa 
vert natural to common loganthms 
Since all the quantities of the n^t- 
hand member of this equation can be 
determined, the total cross section g 
niay be calculated 

11.71 If the measurement just de- 
scribed IS to give the sum of the scatter 
iDg and absorption cross sections, it is 
Necessary that the experimental ar 
rangement should satisfy the condition 
ot what IB knmvn as “good geometry ’ 
This means that the dbstance between 
tAe source and the sfa5 of* a6sor6er A, 
iMid between this and the detector 
must be relatively large compared with 
the size of the slab, so that the latter 
subtends small angles at the points 
^here the source and detector are situ 
ated Under these conditions very few 
of the neutrons which are scattered m 
the slab A, and which are distributed 
more or less uniformly m all directions 
reach the detector In order that equa- 
tion (11 6) may give the total cross 
section, It 13 necessary that I should 
be proportional to the number of neu 
trons which pass through A, without 
undergoing any kind of interaction with 
the nuclei present m the absorber If, 
however, an appreciable proportion of 
the scattered neutrons were able to 
reach the detector, this conditionWould 
not be satisfied, and equation (116) 
■Would give an uncertam result, some- 
tlnng between the total and absorption 
cross sections 

11.72 By deliberately altermg the 
mrangernent of source, absorber .and 
detector so as to give “poor geometry* 
a distmction can be made between 
B<iattenng and absorption For ex- 
ample, if the detector is placed at an 
ntigle of 90” from the mcident beam of 
xifeutrons, that is to say, if the detector 



305 


The Nettlrrm 


is in such a position that it can bo 
rcachwl only by neutrons \yhich have 
been scattered through an angle of 90”, 
it is possible, in principle, to determine 
the scat tering cross sect ion. ''Flic differ- 
ence between the total and scattering 
cretss sections gives the absor])t ion crop 
section. If a separation into elastic 
and inelastic scattering is required, it 
may be borne in mind that the latAer 
probably docs not occur with slow neu- 
trons betvau.sc the nuclear e.vcilation 
energy is about 0.1 Mov for hca\- 3 ' 
elenu'nts and of the order of 1 Mev for 
the lighter ones (§ 11.103). Since neu- 
trons arc .scattered fairly equally in all 
direct ion.'5,* the number scattered at a 
particular angle, sa}' 90®, is small; 
lienee, the procedure described here 
rcquin.'S a strong neutron source. 

11.73. Ideally, us indicated earlier, 
it is desirable to determine the cross 
section of each isotopic, constituent of 
a given element. If the latter consists 
of two isotopes only, the problem is 
rebtively simple; by making cross sec- 
tion measurements wth two saraides 
containing different knowm proportion.s 
of the two nuclide.'^, the contribution of 
c‘.ach c.an Ik; evaluated. Tlicrc are pos- 
sibilities even if three Isotopes arc 
}>reFent, provided a .sample which has 
been considerably enriched in one or 
more can be. obtained. 

11.7*1. Another approach, which is 
.applicable to absorjition cross sections, 
has Ix'cn opcuied up by the work, in the 
I'niWi St.ate.s, of A. J. Dempster, one 
of the pioneers of the mass spectro- 
gr.nph (§8,40). Sc.aftering crciss scc- 
tiens, esjjocially with fast ncutron,«, do 
not usually var>' markedly from one 
isotope to another, but the ab.sorption 
cross sec-lion, s often show striking dif- 
ferences, Hence, it Is in the hUter 
consu-ction th.at d.ata for individual isc>- 


topes are de.sirable; the following pro- 
cedure may then be employed. The 
mass spectrogram of the target ma- 
terial is taken before and after ex- 
po.sure to neutrons; from the change 
in the patterns the relative amounts of 
the various isotopes whicli have taken 
part in the neutron reactions can be 
estimated. A method is thus available, 
at least, in principle, for apportioning 
the obser\^ed absorption cross .sections 
among the various constituents. Fur- 
ther reference to this matter udll be 
made later (§ 11,96). 

11.76, If a neutron absorption proc- 
ess leads to the formation of a radio- 
active nuclide which can be distin- 
guished by its activity, it is frequently 
possible to determine the cross section 
for that particular process. A thin foil 
of the experimental material is exposed 
to neutrons of knoum intensity, and 
after a definite time the radioactivity 
is measured by means of a Geiger- 
Aliillcr or similar counter. From the 
number of counts, associated wnth the 
specific product, the amount of the lat- 
ter formed by the neutron reaction 
can be determined. In the calculation 
a correction must be made for the 
dccay-wliich has occurred during the 
period of bombardment. In order to 
evaluate from these data the nuclear 
cros-s section, for the particular neutron 
process, a modified form of equation 
(10.1) is employed. The latter is based 
on the .supposition that there is just 
a single layer of target nuclei, but in 
actual practice allowance must bo made 
for the target of appreciable thickness. 
Nevertheless, by the use of a fairly 
thin foil, it may be supposed that the 
target docs not absorb sufficient neu- 
trons to cause any appreciable attenu- 
ation in the neutron beam. 

11.76. Suppose the neutron source 


•7> ’•ro ftw pirn*! 
tliA*. U. t-y grp'.orii, 


(-xrrplioPAl no5ftWv ihr praUcring of netUrons bv in-d.-tjern nuclei 
vrhich tirp im'vjrSiint in the f tudy of nuclear forces. ' ' 





306 

provides a neutron density of n neu- 
trons per cc moving with a velocity v 
cm per sec , in a given direction, then 
the product nv, expressed in terms of 
number of neutrons per sq cm per 
sec , IS called the neutTon fiux Assum- 
ing negligible attenuation, as postu- 
lated above, this may be regarded as 
being uniform throughout the whole 
thickness of the target foil If the 
latter contains N target nuclei per cc , 
and V IS the volume of the foil, a total 
of NV nuclei are exposed to the neu- 
tron beam The cross section per nu- 
cleus IS ff- sq cm , and ao NVc is the 
effective area of the target material 
Upon multiplying this area by the neu- 
tron flux, the result nvNVa will give 
the number A of target nuclei which 
have undergone transmutation per sec- 
ond, hence, 


Chap XI 
A = nvNVff (117) 

The number A may be identified luth 
the number of radioactive nuclei deter 
nuned above, and hence the cross sec 
tion for the particular reaction leading 
to the formation of this active species 

IS 

"-Jiv 

The absorption cross section for the 
given reaction can thus be determined 
It may be noted that the result ob- 
tained in this manner refers to a spe- 
cific isotopic constituent of a given 
matenal, for it is only this particular 
nuclide which vvill mteract with neu 
trons to yield the product detected. 


Sourcebook on Atomic Energy 


MONOENERGETIC NEUTRONS 


NExn'RON Velocity Selectors 
11 77 In the foregoing paragraphs, 
the general methods for studying nu- 
clear cross sections were outhned, it is 
now necessary to consider the devices 
called velocity selectors, whereby neu- 
trons of definite energy, or velocity, 
may be obtained As stated in § 11 38, 
even thermal neutrons at a given lem- 
anu' 

means must be found for selecting 
those with known energies Virtually 
all the investigations m this significant 
area of neutron physics have been made 
m the United States in recent years, 
and there is every reason to expect that 
this state of affairs will continue m the 
future Three mam techniques have 
been developed for making measure- 
ments with neutrons of specific en- 
eigies, these are the time-of flight ve- 
locity selector, employed largely by 
the nuclear physicists at Cornell and 


Columbia Universities, and at the Los 
.^amos Scientific Laboratory, the me- 
chanical selector, sometimes referred 
to colloquially as a “neutron chopper/ 
used at the Argonne National Labo- 
ratory, and the crystal spectrometer 
developed at the Oak Ridge and Ar- 
gonne National Laboratories Both 
of the latter methods require neutron 
RourcEs nf -h\gh density, such as are 
produced in nuclear fesion reactors 
11.78 The txme-of-fiight velocity se- 
lector owes its ongm to the work of 
L W Alvarez of the Radiation Labo* 
ratory, Berkeley It can be used only 
m conjunction with neutron sources 
which can be modulated in such a way 
that the neutrons are produced in 
short bursts, lastmg only a few xml- 
honths of a second, separated by longer 
intervals Neutron pulses of this type 
can be obtained with the aid of a Im 
ear accelerator (§ 9 45) or a cyclotron 



307 


The Ncvtrm 


fS 9.53), for thr^o instrument? respond 
verj' nipidly when switched on and off. 
Hipii-enerfr}’ particles, stich as protons, 
dcuterons or alpha particles, produced 
in one or other of these devices, arc 
allowed to imynnge on a suitable target 
ao as to produce the requisite neutron 
beam. The neutrons formed in this 
manner generally have high speeds and 
they must first he slowed down by 
pa-HSiigc through a slab of paraffin since 
(he time-of-flight procedure can be 
us<*fl only with slow neutrons. 

11.79. Tiic measurement of cross 
.‘wetions is made by the transmission 
mctho<I based on the arrangenrent il- 
lustrated in Fig. 11.3. However, the 
neutron source is not continuous, but 


l,CUTfiOV 

f’ULSES 


i i] 

W- 1 ^ 

1 

1 

u. 1 ^ 

OCTfCTO*> 

J 





TlUt 


Fto. 11.4. Principle of (he timc-of-niglit 
velocity selector. 

i-s nuKlulatcd, as described above; in 
addition, the deled or i.s also modulated 
that it is sensitive only d\iring 
(.t-rtain periods, corresponding to the 
neutron pvdscs but delayed by a defi- 
nite int<-rval. TJie rolationsliip of the 
neutron pulses to the periods of the 
deteetor sensitivity is represented di- 
agnunmatically in Fig. 11.4, the latter 
l'<’5ng .nhv.ays t sec. behind the former. 
If I cm. w the distance from source to 
ditedor, it is app.arent tli.nt the only 
neutrons which will recister are those 
hav‘u 5 g ti spew! of l/l cm. wr sec. for 
riie*o are the only one.s which can 
O'arli the tlctector while it i.s sensitive.* 


All other neutrons leaving the source 
will arrive during the "dead” period 
of the detector. 

11.80. Tlie neutron intensities I and 
lo at the detector arc determined with 
and without the absorber, respectively, 
and from these the total cross section 
for the neutrons with velocity I/t cm. 
per sec. is calculated by means of 
equation (11.6). B}' altering either the 
distance 1 between source and detector, 
or the time inlen^al t between the 
neutron pulse and the sensitive period 
of the detector, or b^- changing both, 
the velocity of the detected neutrons 
can be changed. Consequently, the 
cross section measurement can be made 
for a number of different neutron 
speeds. Because the distance I cannot 
be too large, nor the time t too .small, 
there is an upper limit to the speed, 
and energjq of the neutrons which can 
be studied by the time-of-flight pro- 
cedure. The practical range of meas- 
urements by this method is from 0.01 
to about 1000 ev.f 

11.81. Tlic vicchanical vciodly selec- 
tor makes use of the fact th.at cadmium 
strongly absorbs slow neutrons noth 
energies less than about 0.3 ev(§ 11.94), 
but certain other metals, such as alumi- 
num, exhibit little absorption in this 
region. A cylinder, made up of alter- 
nate layers of cadmium and aluminum 
nmning parallel to the axis, is rotated 
before a strong .source of slow neutrons. 
This acts as a shutter and only when 
the laminations are parallel lo the neu- 
tron direction, as shown in Fig. 11. .5, 1, 
can the neutrons get through lo the 
defector. However, the detector is not 
Ecn.sitive all the time, bvit just for a 
short period at .a definite interval after 
the neutrons have been transmitted. 


frorn the hei that f U the tim(-^.f.fijKht, from rourcc to 
'‘tkf ’ t«ni;iiUr 5!nnr..a« vhsrh rt .wh ih- dctfctor v.-hil.- it h n^kitive 

• 4.3 X 10' cm. jy-r k-c., ro that it travel^. 



308 Sourcebook on Atdmc Energy Chap XI 

The tuning is achie\ ed by means of a 11 82. Owing tb the diffraction by 
mirror fixed to the rotating cylinder, crystals of neutrons with energy about 
as shown, when this mirror is m the 0 02 ev, as stated in § 11 12, there are 
correct position, as represented in Fig certain directions m which the reflected 
11 5, II, light IS reflected from it on to a neutrons have increased intensities 
photocell i\hich activates the detector The condition for the diffraction max- 
The time t sec , elapsing between the ima may be obtained by combining the 
instant the shutter permits the neu- Bragg equation (2 13), which is also 
trons to pass through and that when applicable to neutron diffraction, with 
the detector is sensitive, is determined the de Broghe equation (3 9) for the 
by the speed of rotation of the cylinder neutron wave length, namely X = 
and also by the relative positions of h/mv, the result is 


DETtCTOR 



NEUTRONS NEUTRONS 


I 1 

Fic 116 The mechanical velocity selector for neutrons of low 
energy 


light source and photocell, all of which 
can be varied If I cm is the distance 
from the source to the detector, the 
<^y isetitr&ss nircfc can he detected 
are, as m the time of-flight method, 
those with a speed of l/t cm per sec 
The absorption cross section for these 
particular neutrons can then be deter- 
mined, m the manner already de- 
scribed, by mtroducmg the absorbing 
matenal at A, m Fig 11 5, 1 Because 
of the limited speed with which the 
cadmium-alummum cylinder can be 
rotated, the time interval t suffers from 
a similar hmitation As a result the 
mechanical velocity selector cannot be 
employed effectively for neutrons of 
high energies 



where, as before, m is the mass of the 
neutron, v its velocity, d is the distance 
between successive reflectmg planes of 
the crystal, h is the Planck constant, 
and n is an integer Since m and h are 
constants, it follows that for neutron 
diffraction by a given crystal, for which 
d 13 constant, the glancing angles 0 for 
maximum reflection are directly re- 
lated to V, the neutron velocities 
11 83 The result just denved forms 
the basis of the crystal spectrometer 



The Neidron 


tmlodiy selceifrr. Slow neutrons frorn an 
intense source are allowed to impinge 
on n crystal, and a detector is placed 
so that the diffracted beam falls upon 
it, as shomi in Fig. ll.G. Neutrons of 
various speeds arc present in the beam, 
but for any arbitrarilj’’ chosen value 6 
of the glancing angle, the great ma- 
jority of the neutrons reaching the 
detector wll have a velocity given by 
equation (11.10). Tlie ciy'stal spacing 
ff is known, and the only uncertain 
factor in tliis equation is the integer iv, 





I'jG. 11. ft. Cr)'.=!tal .'ipcctronictcr velocity 
selector. 

however, except for large glancing an- 
gles, Ibis is almost invariably unity, 
and .‘^o the velocity of the neutrons 
relk'cted at the angle 0 can be calcu- 
lated. nie intensity measured by the 
detector, with and without, the slab A 
of alxcorlver, ]>emiits the nuclear cro.ss 
section of the latter, for the neutrons of 
this particular velocity for the chosen 
value of 0, to bo determined in the 
usual manner. 

11.84., If the glancing angle & is 
cltanged, neutrons with a different ve- 
locity will now reach the detortor, so 
that them will l»e a ninge, or spectrum, 
of tieutrun velocities corre.'^ponding to 
variations in the angle In'twecn the 
neutron beam and the reflecting sur- 


309 

face of the crj^stal. For this reason the 
instrument is sometimes referred to 
as a neutron spectrometer. By making 
transmission measurements, as de- 
scribed above, wdth different settings of 
the angle of the spectrometer, it is con- 
sequently possible to determine the 
absorption cross sections for a range of 
neutron energies. Because the glancing 
angle diminishes with increasing neu- 
tron velocity, the former ultimately 
becomes too small to be measured nitli 
any degree of accuracy. This sets an 
upper limit to the speed, and energy, 
of the neutrons which can be studied in 
the cr 3 'stal spectrometer. The prac- 
tical range of usefulness is found to be 
from about 0.01 to 100 ev. 

SotmCES OF MONOENEnCETIC 
NeU'I’RONS 

11.85. As already indicated, the ve- 
locity selectors described above can be 
employed only for slow neutrons, w’ith 
energies from about 0.01 to 1000 cv, 
i.e., up to 0.001 Mev. It happens that 
this is a particularl}’’ intere.sting energi"^ 
range, but it is nevertheless desirable 
to obtain cro.ss sections for neutrons of 
higher energ}'. No de\'ice analogous to 
a velocit}' .selector has yet been de- 
veloped for the study of fast neutrons, 
but monocnergetic neutron beams of 
certain specific and knorni energies can 
be obtained from some of the sources 
described in § 11.13 ct scq. The photo- 
neutron sources, in wliich gamma rays 
from artificial radioisotopes produce 
neutrons from deuterium or beiyllium, 
are particularly iiscful for this purpo.se. 
For cx.ample, the decay of the 14.S-hr. 
Na-‘ isotope of sodium is accompanied 
I fke emi.ssion of 2.7G-Mev gamma 
rays; if these undergo the {y,n) re- 
I action with beryllium, for which the 
I thre.'^hold energy- is 1.G3 Mev, the cn- 
j ergA- of the re.^-ulting neutrons is about 
i eight-ninths of 2.76 — 1.63, i.e., 1.00 



310 Sourcebook on 

Mev, the remaining 0 13 Mev being 
recoil energy Monoenergetic neutron 
beams, covermg a range of energies 
from about 003 to 1 Mev, have been 
obtamed from vanous photoneutron 
sources 

11.86. Another source of monoener- 
getic neutrons is the Li’(p,n)Be’ re- 
action, the energy of the incident pro- 
tons being carefully controlled As 
stated m Chapter IX, the Van de Graaft 
electrostatic generator can yield pro- 
tons with defimte energies up to about 
12 Mev, and these may be used to 
bombard lithium targets With pro- 
tons of energy which exceeds the thre^- 
old value of 1 88 Mev (§ 11 17) by the 
least practical amount, it is possible to 
obtam neutrons of about 0 05 Mev 
energy, by steadily increasing the en- 
ergy of the incident protons, mono- 
energetic neutrons with energies up to 
3 Mev can be produced 

11 87. Two sources of approximately 
monoenergetic neutrons of still higher 
energies are the reactions Be’(d,n)B“ 
and Li^(d,n)Be*, for which the ener- 
gies are approximately 4 and 15 Mev, 
respectively A newer procedure for 
obtaining monoenergetic neutfons of 
fairly high energy makes use of the 
(d,n) reaction between deuterons and 
tritium absorbed on a zircomum foil 
target, i e , H®(d,n)He* The reaction 
energy m this case is close to 14 Mev 
By the use of accelerated deuterons, 
preferably from an instrument which 
yields particles of fairly uniform en- 
ergy, high-energy neutron beams, up 
to 20 Mev or more, can be made avail- 
able for cross section measurements 
Monoenergetic neutrons, with energies 
exceeding about 30 Mev, are not easily 
obtainable at the present time The ; 
only device yielding possible projec- 
tiles, such as protons or deuterons, of 
really high energy is the cyclotron, but 
the emergent beam must be passed 


Atonac Energy Chap XI 

through a magnetic field to sort out 
particles of umform energy (§ 9 65) 

11 88 At the other extreme, there is 
the problem of obtaining neutrons of 
very low energies In this connection, 
an interestmg procedure, which makes 
use of the diffraction of neutrons by 
crystals, has been devised Consider 
a block of material, such as graphite, 
consisting of a very lai^ number of 
randomly oriented, small crystals A 
beam of thermal neutrons is allowed to 
enter the graphite, and since the many 
crystals are arranged at a great vanety 
of angles, neutrons of a considerable 
range of velocities, as determined by 
equation (11 10), will suffer diffraction 
These neutrons will be reflected from 
one crystal to another, so that very 
few wU escape from the block of 
graphite Ho\n ever, there xs a velocity 
hrmt below which neutrons wll not 
undergo diffraction in the given ma- 
tenal, this lunit occurs when the glanc- 
mg angle $ necessary to produce dif- 
fraction IS 90®, and sm $ is unity Upon 
inserting this value for sm 8 in equation 
(H 10) and taking the integer n to be 
unity, the corresponding velocity is 
found to be h/2dm, where d is the 
maximum spacing of the reflecting 
planes m the graphite crystals, namely, 
3 4 X 10^ cm 

11 89 Neutrons with smaller veloci- 
ties could be diffracted only if the 
glancing angle were greater than 90®, 
which IS impossible Consequently, 
thermal neutrons wth velocities ex- 
ceeding this limiting value ■will be dif- 
fracted and scattered by the material, 
but those with smaller velocities will 
pass right through The graphite thus 
acts as a velocity, or energy, filter, 
which retains nearly all thermal neu- 
trons with velocities greater than h/6 8 
X 10"^ cm per sec The correspond- 
mg kinetic enei^ minimum 
can be readily calculated, and this is 



312 


Sourcebook on Atomic Energy 


processes usually require more highly 
energetic neutrons 
11.93. With neutrons of high enei^, 
in the Mev range, the cross sections are 
low, being less than 10 bams, com- 
pared with possibly hundreds or thou- 
sands for the resonance peaks men- 
tioned above There is usually a grad- 
ual decrease with increasing energy, 
althou^ peaks of a very minor chamc- 
ter have been reported between 0 I and 


Chap XI 

the cross section reaching a maximum 
of 7200 bams at 0 176 ev The cross 
section then drops sharply, with m- 
creasing neutron energy, falhng to 
about 5 to 6 bams at 5 ev, at which 
value it remains approximately con- 
stant nght up to 10 Mev 
11 96. Incidentally, an examination 
of Fig 11 7 shows very clearly the 
necessity for the use of precisely con- 
trolled monoenergetic neutrons in cross 



Fig 11 7 Absorption of neutrons by cadmium, showmg the 
resonance peak at 0 176 ev 


1 Mev for some elements, notably 
oxygen and aluminum 
11 94. The general type of behavior 
may be illustrated with reference to the 
neutron cross sections of cadmium, 
Since this case is of especial practical 
importance The variation of total 
cross section with neutron energy is 
shown m Fig 11 7, the results are 
plotted on loganthmic scales so as to 
make it possible to include the large 
ranges of both cross sections and ener- 
gies An approximate “1/v region” ex- 
tends up to about 0 03 ev where the 
\ total cross secbon is about 2300 bams 
/ This 13 followed by a resonance peak, 


section studies, particularly m the re- 
gion of low energies For 0 1-ev and 
0 25-ev neutrons, the total cross sec- 
tions of cadmium are 3400 and 2400 
baras, respectively, compared with 
7200 bams for neutrons of 0 176 ev 
energy It is evident that a slight 
change in the energy, or velocity, of 
the neutrons has a considerable in- 
fluence on the results obtained in this 
region In such cases cross sections for 
“slowneutrons” are virtually meaning- 
less 

11 96. The study of cadmium has 
proved of interest because it has been 
established that the exceptionally high 



313 


The Neutron 


oro?p section is mainly due to the Cd”® 
isotope; the peak value for this nuclide, 
v.'hich is present to the extent of 12.3 
per cent in normal cadmium, has been 
c.stimalcd at about 20,000 bams. Strik- 
ing proof that Cd"® absorbs neutrons 
very strongly was obtained by A. J. 
Dempster, by the method referred to 
in § 11.74. iConnal cadmium was ex- 
po.^cd to slow neutrons, and after some 
time specimens of the metal from the 
surface, where the interaction with ncu- 


no IIZ 114- 1/6 



Fig. ll.S. Dempster’s identification of 
c.‘ulmium-113 ns the strong neutron ab- 
porlx-r. (From Ph/s. Pev,, 71, S2P (1947)). 

Irons liad occurred, and from the in- 
terior, which liad been jirotected from 
maction, were subjected to mass-spec- 
trographic examination, with the re- 
sult shown in Fig. 1 l.S. It Is seen that 
the isotope of mas.s number 113 has 
essentially disappearcri from the sur- 
face while the proportion of the 114- 
isotope has increased. It is apparent, 
Ihcndore. that the interaction of slow 
ncut rons with cadmium consi.sts largely 
of .an reaction with Cd”*, in 

whidi the latter h converted into Cd”^. 

11.97. Other elements which exhibit 
ivhtively .sharp re.^onance pe.aks for 
.Oow neutrons, with cro.'^.s .sections at- 
t-'-ining Ihou-sands of hams, are the 
fttUowiug: rih^lium (1.3 cv), silver (5.3 
ev), indixun (1..5 ev). samarium (0.1 cv), 
ruropiuju (0.4.5 ev^ iridium (0.05, 1.25 
ev) and gold (4.8 ev). On the other 
hand, the miY-earlh elements gado- 
linium and d>>prfvduin have very high 
ere Cor the absorption of 


neutrons wth energies less than 0.1 ev, 
although no sharp resonance peaks 
have been reported in this region. 

The BnEiT-WiGNTiE Theoey 

11.98. The theory of the absorption 
of neutrons at, and in the vicinity of, 
the resonance peaks was worked out 
by G. Brcit and E. P. Wigner in tbe 
United States in 1936, and the result- 
ing Drcil-Wigncr formula, as it is called, 
has fonned the basis of the interpreta- 
tion of neutron cross sections. The 
fundamental principle involved is simi- 
lar to that described in § 10.64; if the 
energy of the neutrons is stich that a 
compound nucleus can be formed at or 
near one of its energy levels, then the 
probability of capture of these neu- 
trons will be e-xceptionally high. The 
treatment which Breit and Wigner 
found most successful was similar to 
that which had previously been em- 
ployed in connection with the disper- 
sion of light, and so it is sometimes 
referred to as dispersion theory. 

11.99. The actual formula obtained 
from dispersion theory is too compli- 
cated to be given here, but some of the 
general conclusions can be indicated. 
It appears, in the first place, that tlie 
resonance cross section should be pro- 
portional to the square of the neutron 
wave length; accordingto the deBroglie 
equation, tliis wave length is equal to 
h/mv, and so the resonance cross sec- 
tion should be inversely proportional 
to the square of the velocity or, since 
the energy is equal to K inversely 
proportional to the energj'. This is in 
agreement with the observation that 
resonance pcalcs correspond to largo 
cross sections in regions of low energy 
only. As stated above, such maxima 
as arc observed for high-energj’’ ncu- 

{ Irons repre-t^ent cross sections of a few 

j bam'^ compared with thousands for 

I therm.al and slow neutrons. 



314 


SouTcehooh on Atomic Energy Chap XI 


11.100. Another factor \vhich, ac- 
cording to the Breit-Wigner theory, 
affects the cross section, is a quantity 
approximately equivalent to the nidtli 
of the resonance peak In a general 
way, if the peak is broad, covering a 
large energy range, the cross sections 
are likely to be somewhat decreased, as 
compared ^ith the case of a sharp and 
narrow peak The width of the reso- 
nance peak IS inversely related to the 
life of the excited state of the com- 
pound nucleus * Consequently, an ex- 



001 01 <0 0 <00 <000 
NCUTOON CNEflS' I*«l 


Fio 110 Absorption of neutrons by 
boron, with no resonance peak 

cited state of short life, for example, 
>\iU mean a broad resonance peak, and 
hence a somewhat lower cross section 
for that particular energy level 

11 101. It IS of interest in this con- 
nection to consider the variation inth 
the neutron energy of the cross sections 
of boron for the (n,a) reaction ,t the 
results are depicted in Fig 11 9 which 
IS also loganthmic in both directions 
It ivall be seen that at low neutron 
energies the capture cross sections are 
relatively large, indicating the possi- 
bility of resonance absorption Never- 
theless, theie IS no definite resonance 
peak, implying an excited energy state 


of comparatively long life; further, 
since the “peak” is broad, the cross 
sectioM, although large, are not as large 
as those for elements, like cadmium, 
where the resonance peaks are narrow 

11.102. Since the typo of slow- 
neutron reaction undergone by boron, 
namely, (n,a), is different from that 
occurring with cadmium and other ele- 
ments, that is, (n.y), for which there 
are definite resonance peaks, it roust 
be admitted that the relatively high 
cross section for boron, and for lithium 
which behaves similarly, may not be 
due to the resonance effect It is per- 
haps significant, m this connection, 
that the 1/v law, which usually breaks 
down in the resonance region, is obeyed 
by boron over the considerable energy 
range from 0 01 to 1000 ev In any 
event, it is because boron has such 
large cro^ sections for the (n,a) process 
for neutrons of low energy that this 
reaction is used m neutron detectors, 
as described m § 11 25 

11.103. The fact that resonance ab- 
sorption usually takes place wath slow 
neutrons, with enei^ less than 10 ev, 
finds an interpretation along the fol- 
lowing lines The arguments do not 
apply to all nuchdes, but they seem to 
be in general agreement with the facts 
m a number of instances According 
to estimates made by N Bohr, the 
energy level separations of a nucleus 
are approximately of the order showm 
m Fig 11 10 Near the ground state 
the separation of successive levels, for 
an element of moderately high atomic 
weight, IS about 01 Mev, a neutron 
with less than this amount of energj 
undergoes elastic scattering, as men- 
tioned m § 11 61, since it is incapable 
of raising the nucleus from its lowest 


* It may be noted that this inverse rclatioivdiip is an aspect of the uncertainty principle 
mentioned in | 3 45 WTieii Uic resonance peak for a given energy level is narrow, the energy 
can be knonn Mith some ccrtaint}, and hence there will be a large uncertainty in the time 
factor, that is, m the life of the nucleus m tliat state, and vice versa 
t The total cross section, including scattenng, is not very different 




315 


The Neutron 

Scattering Cross Sections 
AKD Nuclear Dimensions 


(ground) sfntc to an excited state. As 
the energy of the nucleus is increased, 
the .‘reparation of the energv* levels de- 
crc.nscs, and in the region of about 8 
Mev the Gucccs.sive levels arc about 
10 cv apart- For still higher energies, 
the succc-'Tsive levels become so close 
that they arc practically continuous, 
11.104. IMien a ncutTon of low, vir- 
tually Kcro, enorg}’ enters a nucleus of 
rnodorate atomic weight, the energy of 
the latter is immedinteh' increased by 
about 8 Mev, due to the binding of the 

rrcic't cr 
CvVt'cv‘»D r.vctcus 





Fjo. 11.10. Schematic rej)re.‘<entation of 
f-epiinifum of energy level.*: in .n normal 
and a comfwuiid (excited) nucleus. 

additional neutron, llio energy levels 
in the resulting compound nucleus are 
now usually about 10 cv apart-, and 
hence a .«mall, additional (kineiic) en- 
erg>' of the incident neutron may pro- 
vide the condition for re.sonancc enp- 
tun'. When several m-'onimce jieaks of 
neutron cros.-^ .sections are obsen’cd, 
thi-'.-e are .-ep.arab.al by energic.s of tbe 
onicr of 10 ev or so, ;us i.s to be cx- 
IMTtiHl. Finally, if ihe neutron has 
1 ^^ev t»r moo^ of kinetic energ}', the 
nuclear energy levels are now so close 
th.at no s^K-eitic peaks can lx? observjxl. 
In a ;-en?-', the absorption of all liigh- 
oiicrgy S'.eatruns is by ^'•‘•'onanre, al- 
tiseugh the erxi'S s>H'tions ar»‘ then vct\' . 

in tuTotviani'e- with the rtsanin*- | 
nun;* u*. the Bri'ii-Wicner formul.a. i 


11.106, For most light elements, and 
for other elements wliich do not exhibit 
resonance peaks in the low-energ)’ re- 
gion, the total cross sections are usually 
les-s than 10 bams. At verj' high ener- 
gies, the total cross sections are small 
for all elements, irrespective of whether 
there arc maxima or not at lower 
energies. Under these conditions, the 
obsen'ed cross sections are virtually for 
scattering only, since the absorjition 
cross sections are then verj' small. 
Scattering cross sections detcmiined in 
this manner with 20-Mev neutrons re- 
veal an interesting fact; whereas the 
absorption (and total) cross sections 
vary in an apparently haphazard man- 
ner from one clement to the next, the 
sc.attcring cross sections increase regu- 
larly with increasing atomic weight or 
mass number. Tliese cross sections are 
directly related to A"'®, where A is the 
mas.s* number, and if, as is very' prol> 
able, they represent actual cross-scc- 
tional areas it follows tliat tbe 
nuclear radius r is proportional to 
From scattering croi^s section measure- 
ments made with a number of elements, 
it appears that tbe nuclear radii are in 
satisfactory agreement with the for- 
mula 1.5 X 10~*®A''® cm., which was 
found to fit the requirements of the the- 
ory of alpha-particle emission (§ 7-32). 

11.106. According to the foregoing 
arguments, the actual cros.s section of 
n nuclcu.s is not very different from 
the value for neutron .scattering deter- 
mined at high energies, namely, from 
2 to ') barn-s. If this i.s the case, then 
an obvious question may be asked; 

j How i.s' it po.s.sib!e to account for the 
i oh*:erved cro.^s sections of .several fhou- 
■ sand baps? A cro.-'s section of 10,000 
bams, for example, would mean a 
inmlear radium cluse to 10“^- cm., in- 
stead of the accepted value of approxi- 



316 


Sourcebook on Atomic Energy Chap XI 


mately 10~‘* cm The explanation of 
these results can be found m the ■wave- 
particle duahty of matter or in the 
imcertamty principle, both of which 
are aspects of the same fundamental 
law of nature (§ 3 45 et seg ) 

11 107. Accordmgto equation (11 5), 
the wave length of a 20-Mev neutron is 
about 0 6 X 10““ cm , which is of the 
same order of magnitude as nuclear 
radii Interaction between the neutron 
and a nucleus can then be regarded 
from the standpoint of classical me- 
chanics, and the scattenng cross section 
IS virtually identical ^vlth the geometri- 
cal nuclear cross section But with 
very slow neutrons the conditions be- 
come quite different The wave length 
associated with a 1-ev neutron is 
2 87 X 10“® cm and such a neutron 
can no longer be treated as a point 
particle colliding vnth a nucleus but 
rather as a wave which can engulf 
man> nuclei The measured cross sec- 
tion m these circumstances is not 
strictly that of the nucleus, it is more 
reasonable to consider it as tbe area 
surrounding a nucleus, within which a 
neutron is likely to be capable of inter- 
acting with It 

11 108 The situation may be con- 
sidered, alternatively, from the stand- 
point of the uncertainty principle 
Accordmg to this pnnciple, if the speed 
of a particle can be estimated with 


some exactness, its position wall be 
knowTi less defiiutely The smaller the 
speed of a neutron, the more precisely 
can it be known, and consequently the 
greater is the uncertainty m its position 
Hence, instead of bemg located at a 
definite point, the neutron may be 
re^rded as having a large effective 
area 

11 109. It is of interest to mention 
that scattermg cross sections deter- 
mined with approximately 100-Mev 
neutrons, obtained by the “stripping” 
of 2(K)-Mev deuterons, are appreciably 
smaller than those for 20-Mev neu- 
trons, especially for the lighter nuclei 
For 270 to 280-Mev recoil neutrons, 
produced by 350-Mev protons, the 
cross sections are smaller still At these 
high energies, the neutron wave length 
IS 0 2 to 0 3 X cm , which means 
that the neutron behaves as such an 
extremely small particle that there is a 
distinct probability it 'WiU pass right 
through an atomic nucleus, without 
being affected The nuclear cross sec- 
tion thus appears to be smaller than 
would be the case for ordinary scatter- 
mg The sinking vanation m nuclear 
cro^ sections for interaction ■with neu- 
trons serves to emphasize the point 
that classical ideas of size do not have 
real significance when applied to the 
lightest particles of matter 



Nuclear Structure and Nuclear Forces 

Chapter XII 


IvUCLEAR BINDING ENERGIES 


Tiie Packing Fkaction 

12.1. From time to time in the course 
of the preceding chapters it has been 
indicated that pne of the prime pur- 
poses of atomic studies is to obtain 
information which will make it pos- 


Packing Fraction = 


variabl 3 '’ differ from integers by small 
amounts. When F. W. Aston, in 1927, 
showed this to be the case, he ex- 
pressed the deviations in the form of a 
packing fraction for each isotope, de- 
fined by 


to to E i g - WoiSht - MossNu mbe r 

Ma.ss Number ’ ' 


piblo to understand the fundamental 
basis of nuclear structure. Such an 
understanding is imperative if full use 
i.s to Im? made of the potentialities of 
the atomic nucleus, either ns a source 
of cnerg}' or as a means for providing 
knowledge that will contribute to the 
cnridunenl of human life in various 
ways. In the present, chapter an at- 
tempt will bo made to gather together 
certain facts, some of wliich have been 
mcntiontHl in earlier portions of this 
b<Kik, and to .see what conclusions may 
be drawn from them regarding the 
forces determining nuclear stability, 

12.2. It w.as recorded in § S.58 that 
.although isotopic weights, as doter- 
minwl by the mass spectrograph, and 
by other methwh? (§9.33), are close 
to whole numlvers, they almost in- 

* In ntii'n thi‘ sabject <i{ ifntojKs w) 

nsvJS E, I). 3Vil,H,n, in the United Su 
’"{’-wV.inir the perrentapr' 

s^pplir^blr to 'rhen; it 


where the isotopic weight is tlie actual 
mass of the isotope (or nuclide) on the 
phj'sical atomic weight scale (§ 8.59), 
and the mass number is the nearest 
integer. The difference between the 
isotopic weight and the mass number 
is frequently called the macs defect, 
although it is not a satisfactory name, 
as will be seen below. Tliis difference 
divided by the mass number gives the 
first term on the right-hand side of 
equation (12.1), and some writers refer 
to this quantity as the packing frac- 
tion. However, since it is so small, 
Aston multiplied the result by 10,000, 
so as to obtain figures which were 
easier to record.* 

12.3. IVlicn plotted against the cor- 
responding mass numbers, the packing 
fractions of nearly all the stable nu- 

s in the early atages of development, \V. D. 
iea, defined a quantity, nhich they called the 
deviation of atomic weiphts from rchole num- 
(ippejircd that the element occurred as a dngh; 

i" 



318 


Sourcebook on Atomic Energy 


cbdes studied, with the exception of 
He*, C** and 0^*, fall on or near to a 
curve of the form shown m Pig 12 1 
Qliere are certain deviations from this 
curve, but they are of a relatively 
minor character which may be ignored 
for the present It la seen that the 
packing fraction is high for elements of 
low mass number, apart from the he- 
lium, carbon and oxygen isotopes men- 
tioned above, but it decreases rapidly 
with increasing mass number Then, 


CAap XU 

supplied m order to break up the nu- 
cl^, it appears that a negative pack- 
ing fraction implies exceptional nuclear 
stability On the other band, a positive 
packing fraction suggests that the nu- 
cleus is somewhat less stable "With 
these conclusions m mmd, an examina- 
tion of Fig 12 1, m a qualitative rather 
than a quantitative sense, indicates 
that the nuclides He*, C'* and 0’« are 
veiy stable, as compared wth other 
species m the same atomic weight re- 



after passing through a comparatively 
flat minimum, the packmg fraction com- 
mences to mcrease slowly but steadily 
12 4 It will be shown m the next 
section that packing fractions do not 
have a precise theoretical significance, 
nevertheless, they do give an indication 
of a fundamental nuclear property A 
negative packing fraction means that 
the isotopic weight is less than the 
nearest whole number, and this sug- 
gests there has been a conversion of 
mass into energy in the formation of 
the particular nucleus Since this same 
amount of energy would have to be 


gion In the intermediate range of 
atomic weights, the packing fractions 
are negative, sho^vlng that the nuclei 
are stable, but the steady change lead- 
ing to positive fractions for elements 
of high mass number, is in harmony 
with the observed instabihty of such 
elements, as is manifested by their 
radioactivity 

Determination of 
Binding Energies 
12 6. With the discovery of the neu- 
tron and the development of the theory 
that nuclei consist of neutrons and 



319 


Nitckar Slmciurc and Nuclear Forces 


protons, it has become clear that Iho 
packing fraction, ns defined by equa- 
tion (12.1), is merely a way of stating 
certain experimental facts, namely, the 
deviations of isotopic weights from in- 
tegral values. As a rc.sult, the relation- 
.ship between the packing fraction and 
nuclear .suability outlined above, can 
be regarded as more or le.ss satisfactory 
from a qualitative point of view only. 
A more exact treatment is to consider 
the difference between the isotopic 
weight, and the total weight of the 
individual electrons, protons and neu- 
trons which make up the atom; it is 


This quantity may be regarded as the 
loss of mass or, more correctly, the 
ma-ss whicli would be converted into 
energ3q if a particular atom were to be 
assembled from the requisite numbers 
of electrons, protons and neutrons. 
The same amount of energj^ would be 
required to break up the atom into 
its constituent particles, and hence the 
energ}' equivalent of the true mass de- 
fect is taken as a measure of the bind- 
ing energy. Tims, if wn, wi„ and ilf 
are expressed, as usual, in physical 
atomic weight units, the binding en- 
erg}' in Mev is given by 


Binding energj* in Mev = 931 [Zmn -f (A — Z)m„ — (12.3) 


Ihi.s quantity which is the tnie m.ass 
defect. 

12.6. If, ns in previous chapters, the 
atomic number of an clement is rep- 
resented by Z and its mass number 
by A, then the nucleus, according to 
accepted vicw.s, consists of Z protons 
and A — Z neutrons. In addition there 
are 51 cxtranuclear, or orbital, elec- 
trons, to balance the charge of the 
Z protons. The constituents of the 
atom are con.‘=cquontly Z protons .and Z 
electrons, which are equivalent in ma.ss 
to Z hydrogen atoms,* and A — Z neu- 
trons, and their total nur.'is is Zmu 
(A — Z)m„, where nin and rep- 
the masses of the hydrogen atom 
.and of the neutron, respectively. If 


according to equation (3.22). The 
binding energj'- of the electrons to the 
nucleus may be neglected or it may 
be regarded as included in the Zmji 
term, so that equation (12.3) is a meas- 
ure of the binding energy of the con- 
stituent particles in the nucleus of the 
given atom.t 

12.7. Tlic nature of the results ob- 
tained may be illustrated by reference 
to two specific examples. The masses 
of the hydrogen atom and of the neu- 
tron .are 1.00813 and 1.00897, respec- 
tively, on the physical atomic weight 
scale, and hence for the joNe-° iso- 
tope of neon, whose isotopic weight is 
19.9988, and for which A is 20 and 
Z is 10, the binding energj' is 


9311(10 X 1.00813) -1- (10 X 1.00897) - 19.9988] = 160 Mev. 


the cxijcrimcntally detemiined isotopic 
weight is M, then the true ma.ss defect 
h defined bv 


For bismuth, with atomic number 83 
and mass ntunber 209, the isotopic 
weight is 209.055, and hence the bind- 


True mass defect « Zm^ -f (A - Z)m„ - 31. (12.2) 

♦ Tfw nilayU' cJi&r.Kf in rojV? which may conmrably orcompanv the formation of a 
Mom from a pro'.on and an electron w neglected. ’ o. a 

h Iv- tfiat an r'.-k'r.tia!)y fimiLar methwl was in f -t.-JO to ealcukte the 


■Ai 


r'": ^ inruiwj jn $ to Calculate the 

«. toe alpha pa.mdc. The rc-.-iryj nro.x-dvjrc, utiHsitig the binding cnerm- of 
uerwe. fit .rrmin«5i'i|-^nnt.'r.‘alh', employed todrrive th" ina«> of the neutron {| 10 5) 



320 


Sourcebook on Atomtc Energy Chap XII 

mg energy, expressed to three signifi- | where the results are plotted against 
cant figures, is j the respective mass numbers With 

931[(83 X 1 00813) + (126 X 1 00897) - 209 055] « 1630 Mev 


The bmdmg energy of the neon (Ne”) 
nucleus is thus 160 Mev, and that of 
the bismuth (Bi^®) nucleus is 1630 Mev 
It IS of particular mterest to note that 
if these energies are divided by the 
appropnate mass numbers, 20 and 209, 
the results are 8 0 and 7 8 Mev, respec- 
tively The mass number is equal to 
the number of nucleons, i e , the total 
number of protons and neutrons, and 


the exception of He*, and 0“, the 
values fall on or m proximity to a 
single curve The binding energies of 
some of the hghter nuclides, such as 
H* and He*, are very low, but over a 
very considerable range of mass num- 
bers, the binding energy per nucleon 
IS close to 8 Mev This is the figure 
us^ in earlier chapters for the average 
energy associated with the attachment 



hence the quantities just determined 
represent the binding energy per nucleon 
m each case These are seen to be 
approximately equal, in spite of the 
fact that the two nuchdea he almost 
at the extremes of the atomic wei^t 
scale 

12 8 An examination of the values 
for the binding energy per nucleon m 
the stable nuclides, for which the neces- 
sary data are available, has revealed a 
stnkmg regularity shown m Fig 12 2, 


to, or removal irom, a nucleus of a 
neutron or proton 

12 9 A closer study of the curve in 
Rg 12 2 reveals that the binding en- 
eigy has a broad maximum close to 
8 4 Mev per nucleon, m the mass num- 
ber range from about 40 to 120 For 
higher mass numbers the value de- 
creases and has fallen to 7 5 Mev per 
nucleon for uranium It is this dimi- 
nution in binding energy which is the 
fundamental cause of the release of 




321 


Nvchnr Siructvre and Nnclcar F orces 


the onormoiiR amounts of energy* ac- 
companying the fission of nuclei of 
high mfiss niimbcr, as will he seen in 
Chapter XIII. 

12.10. It may he remarked tliat al- 
though Fig. 12,2 is important and use- 
ful, it doc-s not give a complete picture 
of the variation in binding cnerg 3 ’. 
The value.s plotted are the average bind- 
ing energy per nucleon for all the pro- 
tons and neutrons present in the partic- 
ular nuclcu.s. But it is evident from 
the shape of the curve that the actual 
binding energj' i.s not the same for 
each nucleon. As the maximum of the 
curve i-s passed, almo.st cverj' succes- 
sive proton or neutron is bound less 
tightly than those already present, so 
that the over-all average decreases 
steadily. What is desirable, but is as 
yet only partly available from isotopic 
weights, i.s the binding cnerg}' of ever}' 
stable, and even unstable, nuclide, so 
that tlie binding cnergv' of each added 
proton or neutron could be determined 
throughout the whole mn.ss range. A 
rea-Ronnhly good c.slimate of thc.se quan- 
titie.s can, however, he made by cal- 
culation, and some of the information 
obtained in this manner will be dis- 
cuss(h 1 later. 

12.11, A matter to which attention 
m.ay l>e called here i.s the problem 
of radioactive decay l)y alpha-particle 
cmi.ssion. .-\lthough both light and 
heavy radioelcmcnts exhibit beta activ- 
ity, the emission of alpha particles is a 
r.nre occurrence among the lighter ele- 
ments.* This fact can be correlated 
with the binding energies derived from 
isotopic weights. The formation of an 
alpha particle from two protons and 
two neutrons would releas-e 2S.2 Mev 
of encrg\-. as seen in § 4.40; hence, if 
the enetgv' rvqulrod to detach two pro- 
ton.s and two neutrons from a nucleus 


were less than this amount, radioactive 
decay by the expulsion of an alpha 
particle should be theoretically pos- 
sible. However, if the decay is to take 
place at an observable rate, at least 
from a nucleus of high atomic number, 
the alpha particle must have about 
5 Mev energ}', so that it has an ap- 
preciable probability of penetrating the 
electrostatic potential barrier (§ 7.31). 
Hence, for alpha-particle emission to be 
detected, the detachment from the nu- 
cleus of two protons and two neutrons 
should require no more than approx- 
iraatelj’’ 28 — 5 — 23 Mev. 

12.12. The total binding energ}' of 
bismuth (Bi*®), as seen above, is 1030 
Mev, and that of uranium (U-®®) is 
1785, so that in this range of mass 
numbers, the mean binding energj’- 
per additional nucleon is 1785 — 1630 
= 155 Mev', divided by 238 — 209 
= 29, i.e,, 5.3 Mev. The energj’- neces- 
sary to detach two protons and two 
neutrons from an atomic nucleus would 
thus be about 21 Mev, which is less 
than the maximum for alpha-particle 
emission. It can be understood, there- 
fore, why this type of radioactivity is 
common among elements •with mass 
numbers exceeding 210. If the same 
calculations are made for elements with 
atomic numbers somewhat less than 
that of' bismuth, it will be seen that 
the mean binding cnergj’’ per nucleon 
is greater than 6 Mev, and conse- 
quently radioactive decaj' by the ex- 
pulsion of alpha particles is not gen- 
erally observed. 

12.13. It was stated in § 10.99 that 
a few alpha-emitters with mass num- 
bers in the region of 150 have been 
detected. In these neutron-deficient 
nuclide.s the number of protons, com- 
p.'ircd to that of neutrons, is nndoubt- 

j odly much higher than for stable spe- 


?■ pc»=:*ib!y ?^-hich is feeWv radioactive, 

6..-3 R .c-!*- radircmcljdes of mrKkrate nvasa numlscr arc slpiis-ective (I'lO.tK)). 



322 Sourcebook on 

cies of similar mass number It mil 
be seen later (§§ 12 21, 12 59) that this 
^\ill result in a considerable decrease 
m the binding energy, so that the re- 
moval of an alpha particle evidently be- 
comes possible Another factor, which 
will be mentioned in § 12 34, probably 
facilitates this type of decay m the 
cases under consideration 

Proton-Neutron Forces 
12 14 The next matter to consider 
IS the nature of the forces which bind 
together the protons and neutrons in 
atomic nuclei One thing is certain 
these forces are essentially different 
from the more familiar gravitational 
and electrostatic forces of attraction 
The small size of the nucleus and its 
great stabihty show that the nuclear 
forces are nhat are knoira as shorts 
range forces, operating over very short 
distances only This distinguishes them 
from the forces associated uith gravi- 
tational and electrostatic fields, which ' 
can act over relatively long distances i 
Further, if long range forces i\ere oper- 
ative, so that there were interactions ' 
between distant nucleons, as well as | 
those in close proximity, the total bind- 
mg energy would mcrease roughly as ! 
the square of the number of particles , 
m the nucleus \ctually, as stated m ' 
the preceding section, the binding en- | 
ergy is approximately proportional to 
the number of constituent nucleons 
This IS attributed to the saturation 
character of the short-range nuclear 
forces of attraction, which are, m some 
respects, similar to the chemical forces 
bmdmg together the atoms in a mole- 
cule In the latter case, each atom is 
firmly bound to a limited number of 
other atoms in its immediate vicinity, 
by the so-called valence bonds, while 
the force between nonadjacent atoms 
IS relatively small Thus, chemical 
bmdmg is a type of saturation force 


Aiotmc Energy Chap XII 

An analogous situation probably exists 
within the nucleus, each neutron and 
proton being strongly held by a lim- 
ited number of other nucleons adjacent 
to It Since the bmdmg energy per 
nucleon is greater m the alpha particle 
than m other light nuclei, it appears 
that two protons and two neutrons 
form a saturated system 

12 16 The existence of proton-neu- 
tron (p-n), proton-proton (p-p) and 
neutron-neutron (n-n) forces of attrac- 
tion can be readily proved by consid- 
eration of a few simple nuclei The 
relative stability of the deuteron made 
up of one proton and one neutron, 
shows that the (p-n) force has appreci- 
able magnitude Further, the addi- 
tion of an extra neutron, to form a 
tntium (H*) nucleus, or of an extra 
proton, to yield the helium (He*) nu- 
cleus, is accompanied by a marked 
mcrease of binding energy, partly due 
to (n-n) and (p-p) forces, respectively 
Since the nucleus of tritium contains 
a proton and two neutrons, it may be 
assumed that there are two (p-n) and 
one (n-n) forces, on the other hand, 
the He* nucleus consists of two protons 
and a neutron, so that there are two 
(p-n) and one (p-p) forces The bmd- 
ing energy of the former, as calculated 
from its isotopic weight, is 8 37 Mev, 
and that of the latter is 7 63 Mev, 
both being appreciably greater than 
the binding energy of the deuteron 
(2 21 Mev) 

12 16 It would appear from the 
binding energies that the (n-n) force 
IQ tntium exceeds the (p-p) force m 
He* by 8 37 - 7 63, i e , 0 74 Mev 
Howe^ er, from a vanety of considera- 
tions, the conclusion is drawn that the 
attractive (n-n) and (p-p) forces are 
virtually equal, but that the latter is 
decreased to some extent by electro- 
static repulsion between the protons 
This view finds some support in the 



323 


in'clcar Siriiclurc and Nuclear Forces 


rojnnrkahlc constancy of nuclear den- 
fiticK. Afi stilted in § 4.19, the radius 
of any nucleus h approxinuitely propor- 
tional to and so the volume varies 
directly ns A, the nw?.? number. The 
miclcar density, wiiich i.s detennined 
by tUe mass divided by the \'olumc, is 
tiius very nearly the .same for all nu- 
clei. irrespective of the number of pro- 
ton.'i and ncutron-s they contain. Such 
a rc.sult indicates an approximate equal- 
ity of the attractive forces operating 
bet ween the individual nucleons. 

12.17. In order to account for the 
det idled experimental facts, it has been 


found necessary to assume that the 
(p-n) force is .somewhat greater than 
eitlicr the (p-p) or («-n) forces. The 
deiitcron, for example, consisting of a 
proton and a neutron, is relatively 
stable; on the other hand, the di- 
neutron, a combination of two neu- 
trons, may have a transitory existence 
(§ 10.52), while the diproton is un- 
known. Similarly, the He" isotope of 
helium, the nucleus of which would 
consist of two protons, has not been 
identified among cither the stable or 
the unstable nuclides. 


NUCLEAR STABILIIT 


NEUrnoN-PnoTON Ratios 
IN Staiiix Nuclei 

12.18. With the foregoing po.stu- 

late.s in mind, it is of interest; to ex- 
amine the variation with increa.sing 
ma-s-s number of the ratio of neutrons 
to protons in the naturally occurring 
micVides, The experimental re.sult,s arc 
plotted in Fig. 12.3, with the numbers 
of protons {Z) ns absciss.ae and the 
numbers of neutrons {A — Z) as ordi- 
nates. A line is drawn at an angle of 
■1.5'', .s() tliat points lying on this line 
repre-tent nuclei cont.nining equal num- 
Ivers of protons and neufron.s. It will 
l)e ob.‘<erved tlml- for element.s of low 
inas.s number, the neutron-to-f)roton 
ratio for the st.able nuclide-s is close 
to unity.* Hd-s Is tvhat is to be ex- 
ivected if the and [n-n) force.s 

are approximately equal, while the 
(p-nl forces am somewhat larger. 

12.19. If the (jh-p) and (n-n) foree.« 
differed appan^Lably, it U probable that 
eiiher protorw or neutrons, respect ively, 
would pr«lo:nin.ate in .‘••table luidoi, 
t'specirdiy for thelighter element.’?., when 

Latt iht numb 


the electrostatic forces arc negligible. 
Similarly, if the (p-n) forces were less 
than those due to (p-p) and (n-n) inter- 
actions, stable nuclei probably would 
con-sist mainly of protons or neutrons. 
If, as .suggested above, the (p-n) forces 
are the largc.st, the maximum binding 
energy and, consequently, live greatest 
stability, would be achieved when the 
numbem of protons and neutrons are 
approximately equal. 

12.20. A further examination of Fig. 
12,3 shows that when the number of 
protons (or neutrons) in the nucleus 
is greater than 20, the ratio of neutrons 
to protons in stable nuclides is always 
larger than unity. In other words, in 
order to maintain stability the niunber 
of neufrons must exceiki the num- 
ber of protons, the neutron excess in- 
creasing with increasing atomic num- 
ber or ma.ss number. F or the heaviest 
stable nucHdc.s, such as sPb-’^ and 

the ratio of neutrons to protoms 
Is slightly greater than 1 .5. 

12.21, The explanation of this fact 
Is not far to seek. As indicated above, 


tbtf rwmbjr of protor.-?, jwd the nude-ar dwrve. w upnroxiniateK- 



324 


Sourcehook on Atomic Energy Chap XII 

the electrostatic forces between pro- that the repulsion energy of the pro- 
tons do not exhibit the saturation prop- tons in siBi*” is about ten tunes as 
erty of the attractive nuclear forces, great as that in soCa", which is the 
so that each proton repels, and is re- heaviest stable nuclide with a neutron- 
pelled by, all the others present m the to-proton ratio of umty 
nucleus As a result, the electrostatic 12 22 In order to overcome the in- 
repulsive force grows rapidly as the creasing repulsion of the protons and 
atomic number increases The total mamtam stability m the heaviest ele- 
electrostatic repulsion m a nucleus is ments, the nuclei must contam a larger 
roughly proportional f o Z*/r, where proportion of neutrons The additional 
Z 13 the number of protons, i e , the (n-n) and (n-p) forces, which appear 
atomic number, and r is the radius of to be purely attractive m nature, then 
the nucleus The latter vanes as A”*, partly compensate for the growing 
where A is the mass number, so that proton-proton repulsion Nevertheless, 
the electrostatic repulsion is deter- beyond a certain point, around Z = 50, 
mined by the quantity Z^jA^'^ It is the electrostatic repulsion has increased 
a matter of simple anthmetic to show to such an extent that the binding 



NUMBER OF PROTONS (Zl 

Fig 12 3 Plot of the numbers of neutrons and protons m stable 
nuclei 




325 


N^nclmr S(rtic(ure and Nuclear Forces 


energy per nucleon decreases steadily 
inth increasing mass number, as seen 
in Fig. 12.2; ibis matter will be con- 
sidered more fully in § 12.59 ci scq. 

12.23. In Chapter X frequent refer- 
ence was made to the stability range 
for (he ratio of neutrons to protons; 
that such a more or less definite range 
exi.st.s for each atomic number (or mass 
number) is evident from Fig. 12.3. 
The mo.st abundant isotopes of any 
given element, which are presumably 
the most stable, arc u.sually found near 
the middle of the stability range. It is 
Inio, for reasons which unll become 
apparent later, that a few nuclides 
lying within the range are vmstnblc, 
hut those outside the range are in- 
evitably radioactive. Tliey decay by 
the emis-sion of either negative or posi- 
tive beta-particles, or by electron cap- 
ture, so as to bring (lie ncutron-to- 
proton ratio within the .stability range 
for the particular atomic number. 

Onn-KvuN' Rui.r.s or Xucleau 
St.^uiuty 

12.24. A sur\'cy of the even or odd 
nature of the numbers of protons and 
neutrons in the naturally occurring, 
stable micUde.s, tabulated in § 8,47, 
has brought to light .some interesting 
regul.'irlties. In the first place, it is 
found that nuclei containing even num- 
hers of both protons and neutrons are 
much more common than any others; 
nviclci with an odd number of protons 
and an even number of neutrons, or 
vice ver.-a, equally common, while 
tho-e containing tvld numbers of both 
protons and neutrons are rare. The 

XumWr of 
Proions- 
Ev(‘n Odd 

XinnU r of ; Even 1G2 ,52 

Neutrons Odd ,55 4 


I numbers of the various types of defi- 
nitely stable nuclides are given in the 
tabulation below. From these data it 
may be concluded that nuclei contain- 
I ing even numbers of both protons and 
[ neutrons are the most stable, wdiile 
those wdth odd numbers of both are 
ver}’- unstable. Incidcntallj', the six 
nuclides Si^, Ca« Ti« and 

Fe®®, which are in the former category, 
constitute about 80 per cent of the 
earth’s crust. 

t 12,26. An interpretation of these re- 
sults has been based on the Pauli 
exclusion principle, de.scribed in § 4.64 
in connection with the grouping of the 
extranuclear electrons. As applied to 
nucleons, it maj’’ be supposed that a 
nuclear state or shell can contain both 
protons and neutrons wdiich differ onlj'' 
in their angular momenta or spins 
(§4.79). According to the exclusion 
principle, then, protons can exist in 
the same state only if they have op- 
posite spins, and the same is true for 
neutrons. It follows, therefore, that a 
closed, or complete, n\iclcar state con- 
sists of two protons and two neutrons, 
the spins of each pair being oppositely 
directed. If each nucleon interacts 
strongly with nucleons in the same 
state, hut weakly with those in other 
states, the forcc.s acquire the property 
of saturation which is characteristic 
of nuclear binding. The general con- 
clusion is thn.s in agreement with the 
statement made above that such a 
group of two protons and two neutrons 
constitutes a saturated system. 

12.26. ITie first point to be noted is 
that nuclei consisting of closed shells 
I should lx; c.xeeptionally stable. The 
simplc.st system of thi.s kind i« the 
I alpha panicle or helium nucleus, for 
i this is made up of two proton.s and 
! two neutrons. Other examples are the 
1 nuclei of C‘-, consisting of three, and 
I o; O-'y made up of four closed sholh. 



326 


SouTcehook on Atomic Energy Chap XII 

It may be seen from Fig 12 2 that nuclide with odd mass number shall 
the binding energies per nucleon for be stable or unstable are not altogether 
these species he above the curve so clear, although there are certain as- 
that they are relatively more stable jwcts of the problem that can be under- 
than other nuclei of low mass number • stood, as will be seen later m this 
It IS noteworthy, too, that the most chapter 

abundant naturally occurring elements 12 29. According to the tabulation 
have mass numbers which are multiples given at the begmmng of this section, 
of four there are only four stable nuclear spe- 

12 27. For a nucleus to consist en- cies of the odd-odd type, that is, with 
tirely of closed states, the number of odd numbers of both protons and neu 
protons would have to be equal to the trons These are H*, Li*, and N‘*, 
number of neutrons As already seen, and no definitely stable odd-odd nu- 
that IS possible only for the lighter elide of mass number exceedmg 14 is 
elements With increasing mass num- known, it appears, therefore, that such 
ber, it IS necessary to increase the isotopes are unstable t The cause of 
number of neutrons to maintain stabil- this general mstability, and of the ex- 
ity Next to a closed shell of two ceptions noted, can be explamed m the 
neutrons and two protons, a combma- following manner Each of the four 
tion of two neutrons, with opposite stable odd-odd nuclei has either one 
spuis, wiU be preferred This is anal- proton and one neutron only, as m 
ogous to the pairing which is a well- H*, or one proton and one neutron m 
known feature of the arrangement of excess of closed shells of four nucleons 
electrons in atoms and molecules It In other words, they may be rep- 
can be seen, therefore, that nuclei with resented symbolically as (ppnn),pn, 
even numbers of both protons and where a; is 0, 1, 2 or 3, for H*, Li*, 3'® 
neutrons should be stable, m harmony and N'*, respectively The extra pro- 
with the predominance of such nuclei ton and neutron can thus enter the 
over all others same level, and even if they do not 

12 28 A single particle, especially a interact appreciably with the nucleons 
proton, m excess of a closed shell will m the closed shells, the (p-n) force is 
not be very strongly bound, this ac- sufficient to provide appreciable stabil- 
coimts for the nonexistence of He® and ity to the system Ihe next member 
Li®, although curiously enough, Be* of this odd-odd senes should be F^*, 
13 the only stable nuclide of berylhum but Ibis and subsequent members are 
Nevertheless, over one hundred nu- unstable because the mutual electro- 
clear species of odd mass number, hav- static repulsion of the protons requires 
mg either an odd number of protons the presence of an additional neutron 
and an even number of neutrons, or (or neutrons) for stability The stable 
the reverse, are known The factors nuclides are thus F‘*, Na®* and Al”, 
which determme whether a particular respectively 

• The Be* isotope of berylhumj which should have a nucleus with two closed ehells, is known 
to be an extremely unstable nuclide Although the binding energy ^r nucleon n ould probably 
be greater than for its neighbors la' and Be*, it is evidently not large enough to prevent it 
from breaking up almost instantaneously into two He* nuclei It is perhaps significant that 
protons of m^erately low energy react with Li' according to the process la' -h H* — » [Be*] — ♦ 
He* + He* (Chapter IX) 

t Tnie odd-oda nuclides K** and Lu*'*, which occur in nature, are radioactive, and hence 
are not stable V*® and La’** may also prove to be radioactive 



327 


Nuclear Structure and Nuclear Forces 


12.30. Since extra neutrons are 
needed for spcc)c.s of higher mass num- 
ber, it is possible that odd-odd nuclei 
of the typo ippnn).Knpn might be 
stable. As no shell cun contain more 
than two neutrons, thc.se nuclei should 
really be reprc.‘'ented by the formula 
ippnn) :{p~nn)n, there being a vacant 
place for a proton in the penultimate 
level. 'Ilic (n-7i) interaction in this 
level makc.« no net contribution to the 
binding cncrg>', because it merely com- 
pensates for the proton repulsions, and 
since the additional neutron and pro- 

Even mass number. . 124 

Odd mass number 


until an odd number of neutrons, arc 
not common. A few elements of this 
type have two isotopes, but tin is the 
only element of even atomic number 
(50) with three stable isotopes of odd 
ma.ss number (115, 117 and 119). 

12.32. For elements of even atomic 
number, the mass range of isotopes 
of even mass number is considerably 
greater than it is for those of odd mass 
number. This fact may be illustrated 
by reference to the nine stable isotopes 
of xenon, atomic number 54, wliich 
are as follows: 

126 128 130 132 134 136 

129 131 


tAin are in different levels, this inter- 
action i.s small, so that these nuclei 
arc \ms(ablc. If the extra neutron were 
converted into a proton, and an elec- 
ttYm emitted, or the proton were re- 
placed by a neutron, accompanied by 
the erni.s'-Mori of a positron or the cap- 
ture of an orbital electron, depending 
on ihe cirenmstanoe.s, the resulting nu- 
cleus would be of the oven-even type 
and con.^-equently likely to be stal)ie. 
lienee odd-odd nuclei of mass number 
gre.ater than 14 arc radio.activc, ex- 
hibiting In'ia decay; wlicfher this is 
jhSMt’ive or negative will depend on the 
neutron-to-proton nUio najuired for 
stnlulity in the pRxluct. 

12.31. For the sake of rom]>letone.s.s, 
cert'iia rorwHorics to the foregoing 
wen-odd ge!ieniU7.atio!js will be men- 
tioned briefly. Elements of even atomie 
tiumlw'i fsTYpiently have scvoaii .stable 
i’ oto|K's of even nnws nmnl’cr, .since 
tsie mnnl«*r of neutrons i< then abo 
evt‘n. t Us the other hanil, st.able jso- 
eiersu'uts of even .ntomie nurn- 
E'r r.nd *vid nsa-ss number, that b, 

* ass-r.d- insrr.t^r 

\ -in st-d 4i: ii e 4Js.;H-ntrv‘, p. 
til— 5- 1.-.-*?.-;:!,': *, 


It is evident frons these figures that 
there is a relatively narrow range of 
neutron-to-proton ratio in which the 
nuelidcs of even atomic number and 
odd mas.s number, that is, with an odd 
number of neutrons, are stable. 

12.33, If the atomic number is odd, 
the element luis few stable isotopc-s, 
never more than two, and provided 
the atomic nsimber is greater than 7, 
the ma.s.s numbers are always odd, 
since the number of ncsitrons will then 
Ire even.* In general, irresirectivc of its 
atomic number, no clement, with the 
possible exception of tin, has more 
than two .sfnble i.sotope.s of odd mass 
number; these numbers invariably dif- 
fer by two units. 

12.34. In addition to the normal .sta- 
bility of even-even nuclei, due to the 
pairitig of {rrototis and netitrous, there 
arc naisons for be!ie\dng that nuclei 
eont, 'lining 20, 50 or 82 protons, or 20, 
.50, 82 or 126 neutrons are particularly 
.<'uable. The.se iiiim!a*rs, often referred 
to av “magic numbers,” appear to be 
asst'Kuated with the completion of on- 


If', has .'i-sUjraity o.-nirrinp: of Ta.ns< numb-T 

r.vrV!'r, 1< nvJifO'tiv-, 'Atth tiso crnbdoa of a ar-ga. 



828 


Sourcebook on Atomtc Energy Chap XII 

ergy levels m atomic nuclei, just as bersll3,115andl23,whichivillsliortly 
certam specific numbers of electrons be considered m detail Among the 
are required to fill the orbital electrwi species which occur in nature, the pairs 
levels (§ 4 65) A few facts may be Rb”-Sr*^ and Re^®^-Os'®’ represent iso- 
mentioned which indicate the special bare of odd mass number, but the 
stabihty associated with these num- first member of each pair is radioac- 
bers of protons and neutrons The tive and is consequently not a stable 
elements of even atomic (proton) num- nuclide 

ber m the vicinity of 20 and 60 have 12 36 When the mass number is 
large numbers of stable isotopes, tin, even, there may be two stable isobars, 
for example, atomic number 50, has if they do exist, their atomic numbers 
ten such isotopes Further, it vull be are also even and differ by two imits 
recalled from § 10 131 that m two cases In four cases, with mass numbers of 
of the so-called delayed neutron emis- 96, 124, 130 and 136, three apparently 
sion the products are I^r®® and Xe‘** stable isobars of even atomic number 
These contam 50 and 82 neutrons, are known In two instances of nat- 
respectively, and their exceptional sta- urally occurring triple isobars of even 
bility would account for the fact that mass number vjz , A"-K*®-Ca‘“ and 
their parents, Kr” and Xe‘”, can expel Yb”®-Lu”*-Hf”*, the successive atomic 
a neutron so readily Finally, it is numbers differ by unity, however, the 
probable that when the ne^ly discov- middle nuclide of each set, which is 
sred alpha-emitters of medium mass an odd-odd species, is radioactive The 
number (§ 10 99) decay, the products triplets Ti*'*-V®'’-Cr^® and 
have the stable configuration associ- Ba*** also apparently exist m nature, 
ated with about 82 neutrons It is but the middle (odd-odd) members, 
possible that this circumstance is, at i e , V*® and La^”, respectively, occur 
least partly, responsible for the tend- only m very small proportions and are 
ency for alpha decay to take place probably radioactive 

12 37 Since stable isobars, where 
IsoBAES AND Beta ACTIVITY they exist, differ by two xmits of atomic 

12 35 Isobars, as defined m § 8 15, number, there should be no stable iso- 
are nuclides havmg the same mass bars of elements adjacent to one an- 
number, that is, the same total num- other m the penodic system, for the 
her of protons and neutrons Apart atomic numbers would then differ by 
from isomeric nuclei (§ 10 114), winch unity * Actually, the three apparent 
will not be considered here, isobars exceptions to the rule that there are 
have different atomic numbers The no stable isobars of odd mass number 
number of possible stable isobars for a are also exceptional in this respect 
given mass number is very hmited, and If two adjacent elements have isobanc 
this fact has an mterestmg bearing on nucbdes, then one or the other may be 
the subject of radioactivity by beta expected to be unstable, decaying by 
decay For any odd value of the mass beta activity or by orbital-electron 
number, there is, m general, only one capture 

stable nuchde, so that no stable iso- 12 38 In general, a nucleus will be 
bars exist liiere are three possible unstable if its isotopic weight is greater 
exceptions to this rule, for mass num- thwi the combined masses of two or 

• This IS a fonn of what is known as MaUaueh*» rule, discussed by the Austnan physicist 
J Mattauch in 1934 



329 


Nuclear Slmchtrc and Nuclear Forces 


more particles into "which it mas' be 
subdivided. Such a micleua should dis- 
integrate spontaneou.sly into these par- 
ticle-s, the extra mass appearing in the 
form of cncrg 3 '. As seen in Chapter X, 
negative bcta-<Iccay and orbital-elec- 
tron capture are not restricted by anj- 
niiu^s, or energy, diftcrenccs, apart from 
the possible small mass of the neutrino. 
For positive beta-activitj', however, 
the mass of the parent must exceed 
that of the product b^’ two electron 
masse.?, that is, by about 0.0011 atomic 
weight unit. In each of these three 
types of radioactive decay the product 
has the same mass number as, and 
hence is iaobaric xvith, the parent nu- 
clide, but the atomic number differs 
bj’- one unit. 

12.39. It can be seen, therefore, that 

if there arc two isobars of adjacent 
elements, with i.sotopic weights which 
differ by a small amount, the one with 
the larger m.a.?s will lend to di.sinte- 
grate by beta decay or bj’ electron 
cajituro, forming the nuclide with the 
.smaller mas.s. 'I'he mas.s difference may 
be quite small, n.s i.s the case, for ex- 
ample, with the isobai-s II’ (tritium) 
and He’. The isotopic weights are 
3.017020 {plus the ma.'^s of a neutrino) 
.and 3.017010, re.'ipoct ively, so that the 
m.'iss diiTerence i.s onlj' 0,000013 atomic 
weight units, equivalent to about 0,012 
'^lev. Kevertholess, tritium is radio- 
net iv(‘, .■''inro if luLS the higher i.sotopic 
weight, deenyingtofonu hclium-3, with i 
the envission of a tiegative Ijida-partiole | 
of hi'.v energ>% idmut 0.01 Mev. j 

12.40. Tiig.se :<rpitnents account fnr | 
too virlur.l iione.xistence c'f stable Lso- \ 
bar- o: eiemi-nts rlilTerinc by unitj' in ! 


t i 

'■-nuc uumbe 

r. or rour>‘\ 

rsurneroiip - 

ia- 

'-•ini’. L 

r.twvn (jf pain 

:■ tif i-oluirs i 

of 

adji'.rent el- 

‘niL-nts -.vhiae 

cither 0!u- i 


.and t 

f’ 

n artifa'i.'u , 

tv. 


'T b'git .nr?' s 

c.ch radif.t- . 



I’ut. in a.diii 

ti'-n, thf-ri- ’ 


arc the three example.?, referred to 
above, of apparently stable isobaric 
pairs of elements differing by unity in 
atomic number; these are Cd”’-In“'\ 
In”®-Sn”’ and Sb>='’-Te>=h Unless the 
isotopic weights of the isobars arc es- 
sentially identical, one member of each 
pair mu.st be intriasically unstable with 
respect to the other. It may be that 
the mass differences of these isobars 
are so small that, the beta particle 
energy would be too low for the parti- 
cles to bo detectable. It is probable, 
however, that a large difference in the 
nuclear spins may make the beta tran- 
sition highly “forbidden.” The prox- 
imity of the atomic numbers to 50, 
which represents a particularly stable 
configunation (§ 12.34), may also be a 
contributory factor, 

12.41. It is quite pos.sible that each 
of the three pairs mentioned abox'e 
maj' eventually be found to contain a 
radioactive mfjmbcr. An indication of 
how tbi.s m.ay arise was obtained in 
1919 l\v P. K. Bell, B. H. Kelelle 
nnfi .T, M. Cassidj’ of the Oak lUdge 
National Laboratoiy. They observed 
that the excited state of In”’’*' not 
only undergoes isomeric transition to 
the ground state In”^, with a half life 
of 4.0 hours, but also emits beta parti - 
cles, at the .same rate, to form Sn”h 
It j.s evident, therefore, that In”^ is 
actii.ally im.stablc with respect to 
.Sn>’h The beta decay is, howex-er, 
highl.y "forbidden” bocau.se the nuclear 
s]>in of the former in its ground stale 
is % units, xvhile that of the latter is 
)'< unit, llie cxcitM In*”*, on the 
other imnd, ha.s a nuclear spin of 
unit, and .so the decay to Sn'” is 
"pennitted." Similar differences of nu- 
clear spin may xw.ll account for the 
f.ailure, hitherto, to observe beta decay 
in the ot!u-r two pairs of apparently 
s:able iuljae.'ijt i-'-obara, 

12.-12. It is nov.' necc-'yar.- to try to 



330 


5owrccboofc on Atomic Energy C/iap Xll 

understand why elements of odd mass cfeus, as discussed in § 12 24 el seq 
number have no stable isobars, Tthile If the mass number is odd, then there 
those of even mass number may have will be an even number of protons and 
two such isobars which differ by two an odd number of neutrons, or vice 
umta of atomic number It will be versa, and so for isobars of odd mass 
shown in § 12 59 that the net binding number the odd-even influence on the 
energy of a particular nucleus is deter- bmdmg energy will be essentially con- 
minedbyseveraldifferentfactors.some slant On the other hand, for nucbdes 
of these mil be considered here in a of even mass number there are tno 
qualitative manner, which is sufficient possibilities the numbers of protons 
for the present purpose There is, first, and neutrons may either both be odd 
a positive energy term dependent, to a or both may be even From what has 
fair approximation, on the total num- been said m the preceding section, it is 
ber of nucleons, i e , on the mass num- evident that for a senes of isobars of 
ber, for a senes of isobars, this term even mass number, the odd-odd mem- 
wiH consequently have the same value bem will be less stable, and hence their 
throughout But because the (p-n) bmdmg energies will be reduced, as 
forces are probably larger than those compared with those of the even-even 
due to (n-n) and (p-p) interactions, members 

the attractive force is actually less 12 45. Consider, m the first place, 
than proportional to the mass number the vanation ^*ith atomic number of 
by a quantity related to the excess of the binding energies of isobars of odd 
neutrons over protons m the nucleus • mass number 'ii^e odd-even effect is 
In an isobanc senes the total number constant throughout, and so also is 
of protons and neutrons is constant, the energy term which depends on the 
the neutron excess must consequently number of nucleons Of the other two 
decrease as the atomic number, and energy contnbutions, both of which 
hence the number of protons, increases are negative, one decreases while the 
Thus, the second term which corrects other increases, m magmtude, with in- 
fer the nuclear composition, is a nega- creasing atomic number It follows, 
tive quantity which decreases m mag- therefore, that the total bmdmg en- 
mtude with mcreasmg atomic number eigies for a senes of nuclides of constant 
in a senes of isobanc nuclides (odd) mass number must fall on a 

12 43 The mutual electrostatic re- parabola-hke curve, such as is depicted 
pulsion of the protons also tends to m Fig 12 4 For the sake of reahty, 
dimmish the binding energy, as seen the mass number is taken as 73, and 
m § 12 21, by an amount proportional the atomic numbers range from 30(Zn) 
to Since A is constant for to 34(Se), the correspondmg bmdmg 

isobanc nuclei, the electrostatic energy energies are, however, only quahta- 
wiU have an increasingly larger nega^ lively correct It should be noted that 
live value as the atomic number in- it is the common practice to plot the 
creases bmdmg energies so that the bottom 

12 44. Finally, allowance must be of the curve represents the most stable 
made for what may be called the effect nuchde of the senes, with the largest 
of the odd-even character of the nu- binding energy 

• The excess number of neutrons, equal to (A — Z) — Z, \ e , to A — 2Z, is pometunes 
called the Moiopic number, a name mlroduced Iw W D Harkm3ml921 However, the appella- 
tion ‘ isotopic" does not convey the real significance of the number 



331 


Kurkar ,^{rmUtrc and Kvckar Forces 

12.46. If can be .*--ocn that, in gen- and the atomic number of the prodiict 
end, tlicrc v.iil be one bobar for which will be one unit larger than that of the 
the energy is at, or ne.arest, the hot- . parent in each case. For the i.sobar.s 
tom of the curve; this will bo tlie only of ma.ss number 73, for example, two 
stable member of the. isobaric .serie.s, stages of beta decay are knowm; thus, 
in accordance with the established fact 

that for any given odd ma.'-'s number jsZn'^ siGa*’ s;Ge‘^ (stable), 
there is b\it one .stable species. It 

may happen, in certain circumstances, 12.48. Isobars which appear to the 
that the binding cnergic.s of the nu- right of the lowest point in the binding- 
clidcs are. .such that a pair of adjacent energy' cun'c (Fig. 12.4) contain more 
isobars with clo-scly similar binding cn- protons than the stable species. Hence, 
crgie.s lie near the bottom of the curve, these nuclides decay bj'’ the emis.sion of 



ATOV C 


Fio. 12.4. Properties of isalxaric nuclidc.s of odd ixiass 

number. 

In this event bofhmiglit nppo.ar .st.able, a positive beta particle, or by JC-elec- 
aUhough one is rc.ally unstable unles.s Iron capture, or both, and the product 
the binding energies are identical. has an atomic nnrnber one unit smaller 
12.47. All isobaric nuciide.s, whose than that of the parent. A chain of 
binding energies are Ic-^^s than that of disintegrations may occur until finally 
the .suable one, will lie on the two anns the stable isobar i.s formed; thus, 
of the pambolic curve in Fig, 12.4. ’ ' 

Tliey will l>e unstable, and will dec;iy jiSc'” £.*, nGeP (.stable), 

by the emission of a negative or posi- 
tive beta-p.i.niele or by orbital -electron 12.49. For isobars of even ma-ss num- 
eapture. lljose to the left of the stable Ikw the results arc somewhat different 
sfK'cies. have loweratomicnuml-fcrs and, Ijceause of the inclusion of the odd- 

bcjic.-, hover proiojts; they will conse- even effect. The general parabola-like 
quently exjiilht ncg:>tive l>‘,*ta-aeti\ity, | .«hnpe of the binding energ>' cur^'e with 




332 Sourcebook on Atomtc Energy Chap XII 

increasing atomic number, due to the be unstable respect to those with 
repulsive proton and excess neutron even numbers Hence, no stable odd- 
forces, IS the same as for isobars of odd nuchde should exist * As regards 
odd mass number However, all nu- the even-even species, it is seen that 
cbdes with even numbers of protons there are two isobars near the bottom 
and neutrons have an additional bind- of the lower curve whose atomic mim- 
ing energy, while for those with odd hers differ by two umts These con- 
numbers of protons and neutrons the en- Btitute the stable isobanc pairs, of 
ergies are correspondingly diminished which several are known, containing 



26 31 SO i 

ATOM C NuMOER 


Fia 12 5 Properties of iaobano nucbdes of even mass 
number 

The result is that the points represent- even numbers of protons and neutrons. 
Y mg the former are lowered, while those Since radioactive transitions mvolvmg 
\ indicating the latter are raised, so that the simultaneous emission of two beta 
'two parabolic curves are obtained, as particVea do not occ\iT,t both nuebdes 
shown m Fig 12 5 are stable, although one may have a 

12 60 A number of mterestmg con- greater binding energy than the other, 
elusions, which are m agreement with and hence be the more stable of the 
the established facts, may be drawn pair 

from these curves Since the isobars 12 61 As is the case m Fig 12 4, 
with odd numbers of protons and neu- nuchdes to the left of the stable spe- 
trons he on the upper curve, they wiH cies decay by negative beta-emission, 

• The only definite exceptiojis are H* la*, B“ and N“, mentioned m § 12 29, which con 
tarn equal numbers of protons and neutrons 

t Two cases of double beta decay were reported m 1949 and 1950, but the results await 
confirmation 




333 


Nuclear Siruclure and Nuclear Forces 

while those to the right either eject a and hence the half life should be shorter, 
positive beta-particle or capture an the larger the difference of binding en- 
orbital electron. The isobar at the ergj- betueen the given nuclide and 
bottom of the upper curve is in the the stable member of the scries. In a 
\inique position of being between two chain of beta disintegrations, the half 
.stable nuclei;*^ hence, it should be ca- life should increase more or less reg- 
pablc of exhibiting both positive and ularly as stability is approached, as 
negative beta-decay. It was stated in may be illustrated by the following 
§ 10.91 that a few artificial radionu- example: 

MSld*--* ill!!:!; KTe’^-* ssCs'^ (stable). 


elides arc known which dcca}' in this 
dual manner; they invariably contain 
odd numbers of protons and neutrons, 
and lie between two stable isobars, 
each of which is of the even-even type. 
But in several instances these inter- 
mediate odd-odd species emit either 
positive or nogati^'c befa-partieles, but 
not both. Evidently, one tjqie of decaj' 
takes place preferentially cither be- 
niu.se this leads to the more stable of 

MXe»9 i!r:> 7^^ 

the tW(i possible products, or because 
the other transition is ‘'forbidden.” 

12.62. Althoiigh .specific elomont.s 
have been indieated in Figs. 12.4 and 
12.5, the foregoing di.?cus.sion applies 
quite generally, with a fc'v exceptions, 
to all isobaric series other than those 
of the lowf;st and highest ma.ss num- 
bers. In some c.ase<. scveial members 
of a serins have been irlentificd, while 
in others only a few are yet known. 
It IS ronseriuently po.‘-'.‘:iiile to predict 
the properties of hitherto undi.'^eovcrccl 
rjidiotiarltdcs. In tlib, connection, .a 
■riraple mlationsmp K-tweeu the ludf 
hfe of a p.-irticuliir fpccie.': and its j*osi- 
taui on the binuincH^nergy cisr’.x* is of 
For j'nu>ars of orid 
srcv^’ r.';m5v<-r, tlie isv-tribility i.< greater. 

< U? U'.I' W"..'- ar>> of. ruA 5r. s.=< «>.;< 


It may be predicted, therefore, that 
if the nuclide eoSn’” is ever obtained 
it \rill be found to decay by the emis- 
sion of a negative beta-particle, the 
half life being of the order of a minute 
or less. 

12.63. An analogous effect occurs 
with isobars of even mass number, but 
the regularity is observed only if the 
even-even and odd-odd members are 
taken separately; thus, 

(stable). 

Since this is a scries of oven mass 
number, two stable isobars might be 
expected, the second, differing from 
by two units of atomic number, 
being raNd’*’’. However, the latter i.s 
unstable, pre.sumably because its neu- 
(ron-to-profon ratio lies just outside 
the .stability range. 

12.64. 'While considering the subject 
of the life periods of beta-emitting 
radionuelidc.s, reference may be made, 
in pa.«sinp. to the mirror nuclei mon- 

I tinned in § lO.lOG. Each of the."c sj)e- 
j cies contain.s one proton in oxrc.«s of 
I the number of ncturons, and the in- 
I stabsHty i? presumably to be accounted 
■ for by the electrostatic repulsion of the 
I prisons. With incrfa.«ing atomic num- 
, her thi< repulrion increa.'=-.'.-, so that 



334 


Sourcebook on Atomic Energy Chap XII 

there is an increasing degree of m- has a half life of about a milbon years 
stability reflected in the progressively Minute amounts of the latter may 
shorter half li\ es thus conceivably exist m nature, al- 

12 66 During the past tvo or three though it is unstable The half life 
decades, chemists have been interested of the isotope of mass number 97 is 
in the problem of the occurrence in 93 days, and this undoubtedly does not 
nature of the elements of atomic num- occur naturally 
bers 43 and 61 Claims have been 12 67. A consideration of the stable 
made from time to time to the dis- forms of praseodymium (atomic num- 
covery of these elements, but none ber 59) and of europium (atomic num- 
of these claims has been definitely sub- ber 63), or a calculation of the binding 
stantiated * The situation is, then, enei^es, suggests that the most stable 
that while it 13 not possible to state nuclides of element-61 should be those 
categorically that there are stable forma with mass numbers 145 and 147 The 
of these elements, it equally cannot be existence of the stable isobars «oNd‘“ 
affirmed that they do not exist Never- and of the adjacent elements ne- 

theless, some significant conclusions odymium and samarium, respectively, 
may be reached on this problem in the shows that these forms of element-61 
hght of the discussion of the preceding may be expected to be unstable The 
paragraphs Since element-43 has an isotope of mass number 147 is known, 
odd atomic number, it can have, at and its half life is 3 7 yr , but the one 
most, two stable isotopic forms The of mass number 146 has not yet been 
neighboring elements of the same type, definitely charactenzed (§ 15 73) It is 
namely, columbium and rhodium, exist fairly safe to predict that if it exists at 
naturally only as the single stable spe- alt in nature, it is probably present in 
cies 4iCb** and respectively It infinitesimally small amounts 

would appear, therefore that 97 and 12 68 At this point the question 
99 are the onlj reasonable mass num- may be asked \l^y are 4*Mo"' and 
bers for possible stable forms of cle- 44RU”, m the one case, and «Nd^” and 
ment-43 The same conclusion can be m the other case, stable, while 

reached by means of detailed calcula- the isobaric forms of the elements of 
tions of the binding energies along the atomic number 43 and 61, respectively, 
lines to be indicated in the next section are unstable? It is true that the stable 

12 66. An examination of the table nuclides have even numbers of protons 
0/ isotopes (§S 47) shows that tie e/e- and odd numbers of neutrons, while 
raents molybdenum and ruthenium ex- the situation is reversed with the un- 
ist m the stable forms 42M0” and 44Ru** stable species But, as already seen, 
Since adjacent elements rarely have this should not make a great deal of 
stable isobars, it is very improbable difference to the stability Actuall> it 
that element-43 can have stable nu- does not seem possible to supply a 
elides with these mass numbers As a simple answer to the question All 
matter of fact, both of these isotopes that can be said, at present, is that 
have been obtained artificiallj m van- there are several influences, both posi- 
ous iiajs and have been found to be ti\e and negative, which determine 
radioactive, the ground state of the nuclear binding energies, the net result 
form with mass number 99, however, of these various effects is evidently 

• As stated in § 10 83 radioactive forms of both these elements are now known (see Chapr- 
(er XV) 



335 


Nuclear Structure and Nuclear Forces 


such that the most stable forms of the 
elements of atomic numbers 43 and 
61 are somewhat less stable than the 
isobars of adjacent elements in the 


periodic system. The latter are, there- 
fore, stable while the former are radio- 
active, decaying by the emission of 
beta particles. 


NUCLEAR FORCES 


Calculation of Binding Eneegies 

12.69. In the present section an at- 
tempt will be made to calculate actual 
bin^g energies of atomic nuclei based 
on the factors mentioned in § 12.42 
et sea. Since nuclear forces are of a 
short-range character, with saturation 
properties (§ 12.14), each nucleon well 
be strongty held by those in its im- 
mediate 'sicinity, but will be unaffected 
by the others. As a result, to a first 
approximation, there will be an cMrac- 
iive energy, proportional to the number 
of nucleons in the nucleus; in other 
words, this energy term will vary ap- 
proxhnately as the mass number A, 
so that it can be represented by the 
term aiA, where ci is a proportionality 
constant. 

12.60. The value just derived for 
the energy of attraction is probably 
reasonably correct when the number 
of protons in the nucleus is equal to 
the number of neutrons.' But, since 
most nuclei contain an excess of neu- 
trons, the result is somewhat of an 
overestimate to be ascribed, as stated 
earlier, to the fact that the (p-p) and 
(n-n) forces are smaller than those due 
to the ip-ai} interaction. Statistical 
calculations, which are too diflacult to 
explain here, lead to the conclusion 
that allowance for this corn-position 
effect, as it may be called, can be made 
by including in the binding energy the 
term —affA — 2Zff/A,vrheTeA — 2Z 
IS the neutron excess and oj is a constant. 

12.61. As seen in § 12 . 21 , the long- 
range electrostatic forces due to repul- 
sion of the prrotmte decrease the-binding 


energy by a quantity proportional to 
Z^fA^'^’, hence the contribution of these 
forces can be expressed by —azZ’^j 
where as is the proportionality constant. 

12.62. In addition a term must be 
included here which was omitted from 
the earlier qualitative discussion be- 
cause it is related directly to the mass 
number and consequently is the same 
for a series of isobaric nuclei. In stat- 
ing that the binding energy is propor- 
tional to the mass number, it is tacitly 
assumed that every nucleon has the 
same access to other nucleons. Actu- 
ally, those at the surface of the nucleus 
wiU be less tightly bound than those 
in the interior, so that the binding 
energy is reduced by an amount which 
varies as the surface area of the nu- 
cleus. Since the nuclear radius is pro- 
portional to A^'^, its area is related to 
A^'^, and the surface effect is given by 
a term — C 4 A*/®, where 04 is the propor- 
tionality constant in this case. 

12.63. Finally, in calculating the 
nuclear binding energy, consideration 
must be given to the influence of the 
odd or even character of the numbers 
of protons and neutrons. "Wlien these 
munbers are both even, the nuclei are 
exceptionally stable, and when they 
are both odd the system is particular^ 
unstable. This ma 5 ’- be attributed to 
the pairing, or otherwise, of nucleon 
spins (§12.27); if all the spins are 
paired, as they would be in an even- 
even nucleus, there is an additional 
contribution to the binding energy, 
but if both a proton and a neutron 
with unpaired spins are present, as 



336 


SouTcebook on Atomic Energy Chap XU 


m an odd-odd nucleus, there is a cor- 
responding negative or repulsive effect 
Although no adequate theory has yet 
been developed to deal with this spin 
effect, it appears that the influence on 
the bindmg energies of even-even or 
odd-odd nuclei can be represented with 
sufficient accuracy by a term ±ai/A, 
where the positive sign, implying an 
mcrease in the binding energy, applies 
to the former type, and the negative 
sign, which results m a decrease of 
this energy, is applicable to the latter 
type Nachi containing either an even 
number of protons and an odd number 
of neutrons, or the reverse, have inter- 
mediate stability and the spin con- 
tribution IS taken as zero 
12 64 Upon adding the five terms 
derived above, it is seen that withm 
the hmitations of the foregoing treat- 
ment which, it must be acknowledged, 
IS probably oversimplified in spite of 
its apparent complexity, the binding 


BE (Mcv) = 19 3 


energy (BE) of a nuclide of mass 
number A and atomic number Z is 
given by 

T^ T. . (A - 2Zy z* 
BE =0,4 -o. J 

12 66. In order to utilize this ex- 
pression to calculate binding energies, 
the values of the five constants must 
be known, of these, 03 can be derived 
from electrical theory, but the other 
foul are empincal and must be ob- 
tained from experimental data By 
differentiating equation (12 4) with re- 
spect to Z, with the mass number A 
maintained constant, and setting the 
result equal to zero, the condition is 

* An equation of this type was derived by 


obtained for the maximum value of 
the binding energy, and hence for the 
atomic number of the most stable 
nuclide for a given mass number In 
the differentiation the terms involving 
oi, 04 and as disappear because A is 
ctmstant, and since 03 is knotrn, it is 
poiKible to determme the value of oj 
giving the best fit of a mean curve for 
which the atomic numbers of the stable 
isotopes are plotted against their mass 
numbers Since 03 is zero for an odd- 
even or an even-odd nucleus, the two 
remaining constants ai and m can be 
calculated from the knonn binding en- 
ergies of any tvo nuclides of this 
type, as determined from their iso- 
topic weights (§ 12 7) The spin-effect 
constant 03 is obtained empirically 
from the binding energies of even-even 
nuclei Upon inserting the constants 
denved m this manner, the bindmg 
energy in Mev can be represented by 
the expression 

0 5S5 -15-, - 13 064 >'• ±1^ (12 6) 

12 66 The relative effects of the 
vanous factors on the net binding en- 
eigy can best be seen by performing 


(12 4)* 
A 


the calculations for nuclides of low, 
medium and high mass number The 
results for soCa*®, 6oSn‘^® and a-U**® are 
given m the table, the estimated bind- 
ing energies are seen to be 342, 1004 
and 1796 Mev, compared with the 
values 341, 1009 and 1785 Mev, re- 
spectively, denved from the isotopic 
weights Since the data, in either case, 
are probably not reliable to more than 
three significant figures, the agreement 
T von Weizsacker m Germany m 1935 


Nuclear Structure and Nuclear Forces 
Calculation of Binding Energies (Mev) 


Attraction of Nucleons 

Composition Effect 

Repulsion of Protons 

Surface Effect 

Spin (Odd-Even) Effect 

Resultant Binding Energy 

Binding Energy per Nucleon 

between the observed binding energies 
and those obtained from equation (12.5) 
is very satisfactory. 

12.67. Upon examining the various 
energy terms it will be noted that the 
decreased binding energy per nucleon 
for elements of high atomic number, 
discussed in § 12.9, is due mainly to 
the marked increase in the electrostatic 
repulsion of the protons. It is, conse- 
quently, also the factor largely respon- 
sible for the possibility of alpha-particle 
emission, since this depends_ on the 
decrease in binding energy of the nu- 
cleons, as explained earlier, and also 
for the considerable liberation of en- 
ergy accompanying nuclear fission, to 
which reference will be made in § 13.22. 

Netjteon-Proton Exchange Forces 

12.68. One of the major unsolved 
problems of nuclear science is to ex- 
plain the nature of the forces which 
are responsible for the strong attrac- 
tions of nucleons for one another. An 
adequate description of the attempts 
which have been made to understand 
these forces requires the use of com- 
plex mathematical ideas, but the sub- 
ject is of such fundamental importance 
that it caimot be ignored here. The 
best that can be done, therefore, is to 
try to present the general basis of the 
concepts, and to evaluate their sig- 
nificance within the limitations of an 
essentially nonmathematical treatment. 

12.69. men, in 1932, W. Heisen- 
berg (§ 4.35) suggested that atomic 



5oSn«“ 

92U“« 

-1-560 

+1680 

+3332 

0 

-64.3 

-236 

-68.4 

-296 

-799 

-153 

-317 

-501 

-t-3.2 

+1.1 

+0.5 

342 

1004 

1796 

8.52 

8.37 

7,54 


nuclei were built up of protons and 
neutrons, he tried to account for intra- 
nuclear attractions by making use of 
the idea of wave-mechanical exchange 
forces, which he had previously em- 
ployed with conspicuous success to ex- 
plain the optical spectrum of helium. 
These exchange forces are a direct con- 
sequence of wave mechanics and have 
no equivalent in classical or Newtonian 
mechanics. As applied to the problem 
of proton-neutron interaction, the or- 
igin of the exchange forces may be 
described somewhat along the following 
lines. 

12.70. It is generally accepted that 
the difference between a proton and a 
neutron lies essentially in the fact that 
the former carries an electrical charge 
whereas the latter does not. Consider 
a system, for simplicity, consisting of a 
single proton and a neutron, as indi- 
cated at I, below; the transfer of a 

© © © © 

I II 

positive charge from proton to neutron, 
or of a negative charge from neutron 
to proton, produces the condition rep- 
resented at II. Although there has 
been an exchange of charge, resulting 
in a change of identity of the particles, 
the ^al state II, like the initial state I, 
consists of a neutron and a proton, 
and hence it has the same energ5''. 

12.71. One of the general results of 
the - wave mechanics is that if any 



338 Sourcebook on 

system can be represented by two (or 
more) states with the same energy, 
then tlie actual state of the system, 
which may be regarded as a combina- 
tion of the two (or more) separate 
states, IS more stable than these indi- 
vidual states In other words, there 
is an additional energy contribution, 
referred to as the exchange energy, mak- 
mg the system more stable, it is conse- 
quently equivalent to an attractive 
force, called the exchange force As 
applied to the proton-neutron system, 
wluch can exist in the states I and II 
of equal energy, this means that the 
proton and neutron must attract one 
another, as a result of the exchange 
force 

12 72 If the